Editing 2379: Probability Comparisons

Jump to: navigation, search

Warning: You are not logged in. Your IP address will be publicly visible if you make any edits. If you log in or create an account, your edits will be attributed to your username, along with other benefits.

The edit can be undone. Please check the comparison below to verify that this is what you want to do, and then save the changes below to finish undoing the edit.
Latest revision Your text
Line 8: Line 8:
  
 
==Explanation==
 
==Explanation==
−
This is a list of probabilities for different events. There are numerous recurring themes, of which the most common are free throws (13 entries), birthdays (12), dice (12, split about evenly between 6-sided (d6) and 20-sided (d20) types), {{w|M&M's|M&M}} candies (11), playing cards (9), {{w|NBA}} basketball mid-game victory predictions (9), {{w|Scrabble}} tiles (7), coins (7), white Christmases (7), and the NBA players {{w|Stephen Curry}} and {{w|LeBron James}} (7 each). Themes are variously repeated and combined, for humorous effect. For instance, there are entries for both the probability that St. Louis will have a white Christmas (21%) and that it will not (79%). Also given is the 40% probability that a random Scrabble tile will contain a letter from the name "Steph Curry". There are 80 items in the list, the last two of which devolve into absurdity - perhaps from the stress of preparing the other 78 entries.
+
{{incomplete|Created by LEBRON JAMES THROWING M&Ms AT A KEYBOARD. The table for the explanations of the chances isn't complete, nor is the transcript. Do NOT delete this tag too soon.}}
  
−
The list may be an attempt to better understand probabilistic election forecasts for the {{w|2020 United States presidential election}}, which was four days away at the time this comic was published and had also been alluded to in [[2370: Prediction]] and [[2371: Election Screen Time]]. Statistician and {{w|psephologist}} [[Nate Silver]] is referenced in one of the list items. On the date this cartoon was published, Nate Silver's website {{w|FiveThirtyEight}} was [https://projects.fivethirtyeight.com/2020-election-forecast/ publishing forecast probabilities] of [[Donald Trump]] and [[Joe Biden]] winning the US Presidential election. On 31 October 2020, the forecast described the chances of Donald Trump winning as "roughly the same as the chance that it’s raining in downtown Los Angeles. It does rain there. (Downtown L.A. has about 36 rainy days per year, or about a 1-in-10 shot of a rainy day.)" A day previously, when the chances were 12%, the website had also described Trump's chances of winning as "slightly less than a six sided die rolling a 1". The probabilities are calculated from [https://xkcd.com/2379/sources/ these sources], as mentioned in the bottom left corner of the comic.
+
This is a list of probabilities for different events. There are numerous recurring themes, of which the most common are free throws (13 entries), birthdays (12), dice (12, split about evenly between d6 and d20 types), M&M candies (11), playing cards (9), NBA basketball mid-game victory predictions (9), Scrabble tiles (7), coins (7), white Christmases (7), and the NBA players Stephen Curry and LeBron James (7 each).  
  
−
The title text refers to the song "{{w|Call Me Maybe}}" by {{w|Carly Rae Jepsen}} (cited twice in the list). "MAYBE" is emphasized, perhaps because the probability of getting her phone number correct, as in the last item in the list, is very low. The capitalization could also be a reference to Scrabble tiles, as was previously mentioned in association with Carly Rae Jepsen.
+
Themes are variously repeated and combined, for humorous effect. For instance, there are entries for both the probability that St. Louis will have a white Christmas (21%) and that it will not (79%). Also given is the 40% probability that a random Scrabble tile will contain a letter from the name "Steph Curry".
 +
 
 +
There are 80 items in the list, the last two of which devolve into absurdity - perhaps from the stress of preparing the other 78 entries.
 +
 
 +
The list may be an attempt to better understand probabilistic election forecasts for the {{w|2020 United States presidential election}} which was less than a week away at the time this comic was published, and had also been aluded to in [[2370: Prediction]] and [[2371: Election Screen Time]]. Statistician and psephologist {{w|Nate Silver}} is referenced in one of the list items. On the date this cartoon was published, Nate Silver's website FiveThirtyEight.com was publishing forecast probabilities of Donald Trump and Joe Biden winning the US Presidential election. [[https://projects.fivethirtyeight.com/2020-election-forecast/]]. On 31 October 2020, the forecast described the chances of Donald Trump winning as "roughly the same as the chance that it’s raining in downtown Los Angeles. It does rain there. (Downtown L.A. has about 36 rainy days per year, or about a 1-in-10 shot of a rainy day.)" A day previously, when the chances were 12%, the website had also described Trump's chances of winning as "slightly less than a six sided die rolling a 1".
 +
 
 +
The probabilities are calculated from [https://xkcd.com/2379/sources/ these sources], as mentioned in the bottom left corner.
 +
 
 +
The title text refers to the song {{w|Call Me Maybe}} by Carly Rae Jepsen (cited twice in the list). "MAYBE" is emphasized perhaps because the probability of getting her phone number correct, as in the last item in the list, is very low. The capitalization could also be a reference to Scrabble tiles as was previously mentioned in association with Carly Rae Jepsen.
  
 
==Table==
 
==Table==
Line 22: Line 30:
 
| 0.01%
 
| 0.01%
 
| You guess the last four digits of someone's {{w|Social Security Number}} on the first try
 
| You guess the last four digits of someone's {{w|Social Security Number}} on the first try
−
| There are nine digits in a {{w|Social Security Number}}, but the last four are commonly used as an identity verification factor. (1/10)<sup>4</sup> = 0.0001, or 0.01%
+
| There are 10 digits in a Social Security Number. (1/10)<sup>4</sup> = 0.0001, or 0.01%
 
|-
 
|-
 
| 0.1%
 
| 0.1%
 
| Three randomly chosen people are all left-handed
 
| Three randomly chosen people are all left-handed
−
| The chances of having left-{{w|handedness}} is about [https://www.healthline.com/health/left-handers-and-health-risk 10%], and 10%<sup>3</sup> = 0.1%.
+
| The chances of being left handed is about 10%, and 10%<sup>3</sup> = 0.1%.
 
|-
 
|-
 
| rowspan="2" | 0.2%
 
| rowspan="2" | 0.2%
Line 37: Line 45:
 
| 0.3%
 
| 0.3%
 
| You guess someone's birthday in one try.
 
| You guess someone's birthday in one try.
−
| 1/365 ≈ 0.27%. Taking into account that a person might have been born February 29, the probability with a random guess is slightly lower.  If the guesser knows on which days there are slightly more births (for example, early October, believed to be because of conceptions occurring on the evening of December 31) and which days there are slightly fewer (for examples, holidays on which a planned, pre-scheduled C-section is unlikely to be held), then the probability is slightly higher.
+
| 1/365 ≈ 0.27%.
 
|-
 
|-
 
| rowspan="2" | 0.5%
 
| rowspan="2" | 0.5%
 
| An {{w|NBA}} team down by 30 at halftime wins
 
| An {{w|NBA}} team down by 30 at halftime wins
−
| This calculation, along with all related ones, uses the source [http://stats.inpredictable.com/nba/wpCalc.php NBA Win Probability Calculator]. Entering Q2, 0:00, and -30 into the calculator yields 0.6% .
+
|
 
|-
 
|-
 
| You get 4 M&Ms and they're all brown or yellow
 
| You get 4 M&Ms and they're all brown or yellow
−
| Depending on the source of one's M&Ms in the U.S., the proportion of them that is brown or yellow is either 0.25 or 0.259 .  0.25<sup>4</sup>≈ 0.39%; 0.259<sup>4</sup> ≈ 0.45% . Both are closer to 0.4% .
+
| Depending on the source of one's M&Ms in the U.S., the proportion of them that is brown or yellow is either 0.25 or 0.259 .  0.25^4≈ 0.39%; 0.259^4 ≈ 0.45% .
 
|-
 
|-
 
| rowspan="2" | 1%
 
| rowspan="2" | 1%
 
| {{w|Steph Curry}} gets two free throws and misses both
 
| {{w|Steph Curry}} gets two free throws and misses both
−
| Curry is a 91% career free throw shooter, so the percentage of missing 1 free throw is about 9%. The chance of missing 2 free throws is about 0.8% ≈ 1%.
+
|
 
|-
 
|-
−
| {{w|LeBron James}} guesses your birthday, if each guess costs one free throw and he loses if he misses
+
|{{w|LeBron James}} guesses your birthday, if each guess costs one free throw and he loses if he misses
−
| LeBron James' free-throw odds are ~73% . The odds of him winning on the first round are 1/365, for the second (364/365)(1/364)(0.73), for the third (363/365)(1/363)(0.73)<sup>2</sup>... Summing all of these from 1 to 365 gives us his total odds of winning at any point in the game are ≈ 1.015% .
+
|
 
|-
 
|-
 
| rowspan="2" | 1.5%
 
| rowspan="2" | 1.5%
Line 58: Line 66:
 
|-
 
|-
 
| You share a birthday with a {{w|Backstreet Boys|Backstreet Boy}}
 
| You share a birthday with a {{w|Backstreet Boys|Backstreet Boy}}
−
|Each of the five Backstreet Boys has a different birthday, so the odds that you share a birthday with one is 5/365 ≈ 1.3% .
+
|Each of the five Backstreet Boys has a different birthday, so the odds that you share a birthday with one is 5/365.25 ≈ 1.3% .
 
|-
 
|-
 
| 2%
 
| 2%
 
| You guess someone's card on the first try
 
| You guess someone's card on the first try
−
| There are 52 cards in a normal deck of cards (excluding jokers), so the probability is 1/52, which is approximately 1.9%.
+
| There are 52 cards in a normal deck of cards (excluding jokers), which is approximately 0.019 (2%).
 
|-
 
|-
 
| rowspan="2"| 3%
 
| rowspan="2"| 3%
 
| You guess 5 coin tosses and get them all right
 
| You guess 5 coin tosses and get them all right
−
| The chance of correctly predicting a coin toss is 0.5, or 50%. The chance of predicting 5 in a row is 0.5<sup>5</sup>, or 3.125%.
+
| The chance of correctly predicting a coin toss is 0.5. The chance of predicting 5 in a row is 0.5^5, or 3.125%.
 
|-
 
|-
 
| Steph Curry wins that birthday free throw game
 
| Steph Curry wins that birthday free throw game
−
| Swap out 0.73 for 0.91 in the above calculations to find Steph Curry's odds of winning. This sum yields ~3.04% .
+
|
 
|-
 
|-
 
| rowspan="3"| 4%
 
| rowspan="3"| 4%
Line 76: Line 84:
 
|-
 
|-
 
| {{w|Portland, Oregon}} has a {{w|White Christmas (weather)|white Christmas}}
 
| {{w|Portland, Oregon}} has a {{w|White Christmas (weather)|white Christmas}}
−
| According to Randall's source (from the ''Bulletin of the American Meteorological Society''), the probability of snow cover in Portland is 4%.
+
|
 
|-
 
|-
 
| You share a birthday with two {{w|US Senator}}s
 
| You share a birthday with two {{w|US Senator}}s
−
| At the time this comic was published, 15 days were birthdays for more than one Senator, and 15/365 ≈ 4%.<ref>Rand Paul and John Thune - January 7<br/>
+
| At the time this comic was published, 9 days were birthdays for more than one Senator.<ref>Rand Paul (R-KY) and John Thune (R-SD) were both born January 7. Patrick Leahy (D-VT) and Angus King (I-MN) were both born March 31. Jim Risch (R-ID), Ron Wyden (D-OR) and David Vitter (R-LA) were all born May 3. Dianne Feinstein (D-CA) and Elizabeth Warren (D-MA) were both born June 22. Bob Corker (R-TN) and Joe Manchin (D-WV) were both born August 24. Bill Nelson (D-FL) and Joe Donnelly (D-IA) were both born September 29. Mike Rounds (R-SD) and Jeff Merkley (D-OR) were both born October 24. Pat Toomey (R-PA) and Jim Inhofe (R-OK) were both born November 17. John Boozman (R-AR) and David Perdue (R-GA) were both born December 10.</ref>
−
Chris Van Hollen and Roy Blunt - January 10<br/>
 
−
Tina Smith and James Lankford - March 4<br/>
 
−
Tammy Duckworth and Mitt Romney - March 12<br/>
 
−
Angus King and Patrick Leahy - March 31<br/>
 
−
Jim Risch and Ron Wyden - May 3<br/>
 
−
Dianne Feinstein and Elizabeth Warren - June 22<br/>
 
−
Todd Young and Joe Manchin - August 24<br/>
 
−
Kamala Harris, Brian Schatz, and Sheldon Whitehouse - October 20<br/>
 
−
Jeff Merkley and Mike Rounds - October 24<br/>
 
−
Jim Inhofe and Pat Toomey - November 17<br/>
 
−
Dick Durbin and John Kennedy - November 21<br/>
 
−
Rick Scott and Gary Peters - December 1<br/>
 
−
John Boozman and David Perdue - December 10<br/>
 
−
 
 
−
Based on [https://en.wikipedia.org/wiki/List_of_current_United_States_senators List of current US Senators on Wikipedia] (and processed through [https://bit.ly/2HZeqQs this Google sheet)].
 
−
</ref>
 
 
|-
 
|-
 
| rowspan="2"| 5%
 
| rowspan="2"| 5%
 
| An NBA team down 20 at halftime wins
 
| An NBA team down 20 at halftime wins
−
| Entering Q2, 0:00, and -20 into the NBA Win Probability Calculator yields 5.2% or 5.3% .
+
|
 
|-
 
|-
 
| You roll a natural 20
 
| You roll a natural 20
−
| A natural 20 indicates a critical hit in the {{w|Dungeons & Dragons}} role playing game. "Natural" means that it is the number showing when rolling a d20 (a 20-sided die), as opposed to an overall total of 20 when counting the die roll plus modifiers. There are twenty sides to a d20 die, so 1/20 = 0.05 = 5% .
+
| A natural 20 indicates a critical hit in the {{w|Dungeons & Dragons}} role playing game. "Natural" means that it is the number showing when rolling a d20 (a 20-sided die), as opposed to an overall total of 20 when counting the die roll plus modifiers. There are twenty sides to a d20 die. 1/20 = 0.05 = 5%
 
|-
 
|-
 
| 6%
 
| 6%
Line 110: Line 102:
 
| 7%
 
| 7%
 
| LeBron James gets two free throws and misses both
 
| LeBron James gets two free throws and misses both
−
| James' career free throw percentage is 73%, so the probability of a miss is 0.27, or 27%. The probability of 2 misses is (0.27)<sup>2</sup>, which is about 7%.
+
|
 
|-
 
|-
 
| 8%
 
| 8%
 
| You correctly guess someone's card given 4 tries
 
| You correctly guess someone's card given 4 tries
−
| Assuming you guess four different cards, 4/52 = 0.0769 ≈ 8% . Assuming that you guess the same card, 1 - (51/52)(50/51)(49/50)(48/49) ≈ 7.7%.
+
| Assuming you guess four different cards, 4/52 = 0.0769 ≈ 8% .
 
|-
 
|-
 
| 9%
 
| 9%
 
| Steph Curry misses a free throw
 
| Steph Curry misses a free throw
−
| Curry's career free throw percentage is 91%, so the probability of a miss is 9%.
+
|
 
|-
 
|-
 
| rowspan="2"|10%
 
| rowspan="2"|10%
 
| You draw 5 cards and get the Ace of Spades
 
| You draw 5 cards and get the Ace of Spades
−
| There are 52 cards in a normal deck of cards (excluding jokers), and the Ace of Spades is one of them.{{Citation needed}} The chances of getting the card is 1 - 51/52 * 50/51 * 49/50 * 48/49 * 47/48 which is approximately 0.096, which rounds to the given 0.1 or 10%.
+
| There are 52 cards in a normal deck of cards (excluding jokers), and the Ace of Spades is one of them. The chances of getting the card is 1 - 51/52 * 50/51 * 49/50 * 48/49 * 47/48 which is approximately 0.096, which rounds to the given 10%. <!-- make into math format -->
 
|-
 
|-
 
| There's a {{w|Moment magnitude scale|magnitude}} 8+ earthquake in the next month
 
| There's a {{w|Moment magnitude scale|magnitude}} 8+ earthquake in the next month
−
| Note that, unlike other earthquake examples, this does not specify where the earthquake occurs. From 1905 to 2021, there have been 98 earthquakes magnitude 8+ recorded around the world.
+
|
 
|-
 
|-
 
| 11%
 
| 11%
 
| You sweep a 2-game rock paper scissors series
 
| You sweep a 2-game rock paper scissors series
 
| You have a 1/3 chance of winning the first comparison, and a 1/3 chance of winning the second. (1/3) * (1/3) = 1/9 ~ 0.11 = 11% .
 
| You have a 1/3 chance of winning the first comparison, and a 1/3 chance of winning the second. (1/3) * (1/3) = 1/9 ~ 0.11 = 11% .
 +
|
 
|-
 
|-
 
| rowspan="3"|12%
 
| rowspan="3"|12%
 
| A randomly-chosen American lives in {{w|California}}
 
| A randomly-chosen American lives in {{w|California}}
−
| California is the most populous state in the US. Out of the approximately 328.2 million Americans (as of 2019), 39.51 million live in California. This means that a randomly chosen American has about a 39.51/328.2 ≈ 10.33% chance of living in California. Due to population change and rounding based on different sources, this could be pushed to 12%.
+
| California is the most populous state in the U.S.A. Out of the approximately 328.2 million Americans (as of 2019), 39.51 million live in California. This means that a randomly chosen American has about a 39.51/328.2 ≈ 10.33% of being in California. Due to population change and rounding based on different sources, this could be pushed to 12%.
 +
|
 
|-
 
|-
 
| You correctly guess someone's card given 6 tries
 
| You correctly guess someone's card given 6 tries
−
| Assuming you don't repeat previous wrong guesses, the probability is 6/52 ≈ 11.54%.
+
|
 
|-
 
|-
 
| You share a birthday with a {{w|US President}}
 
| You share a birthday with a {{w|US President}}
−
| Presidents {{w|James Polk}} and {{w|Warren Harding}} share a birthday, and are the only presidents so far (in 2020) to do so. Additionally, {{w|Grover Cleveland}} served two non-consecutive terms and is counted twice (as the 22nd and 24th presidents). He therefore shares a birthday with himself. With 43 distinct birthdays, the odds of sharing a birthday are 43/365 ≈ 12%. (This does not consider February 29 or that more births occur on some days than others.)
+
| Presidents {{w|James Polk}} and {{w|Warren Harding}} share a birthday, and are the only presidents so far (in 2020) to do so, giving the odds of sharing a birthday as 44/365 ≈ 12% .
 
|-
 
|-
 
| rowspan="3"|13%
 
| rowspan="3"|13%
 
| A {{w|Dice#Polyhedral_dice|d6}} beats a {{w|Dice#Polyhedral_dice|d20}}
 
| A {{w|Dice#Polyhedral_dice|d6}} beats a {{w|Dice#Polyhedral_dice|d20}}
−
| The odds of a d6 beating a d20 are (0 + 1 + 2 + 3 + 4 + 5)/(6*20) = 0.125 ≈ 13% .
+
| The odds of a d6 beating a d20 are (0 + 1 + 2 + 3 + 4 + 5)/(120) = 0.125 ≈ 13% .
 
|-
 
|-
 
| An NBA team down 10 going into the 4th quarter wins
 
| An NBA team down 10 going into the 4th quarter wins
−
| Entering Q3, 0:00, and -10 into the NBA Win Probability Calculator yields 12.6% or 12.8% .
+
|
 
|-
 
|-
 
| You pull one M&M from a bag and it's red
 
| You pull one M&M from a bag and it's red
Line 153: Line 147:
 
| 14%
 
| 14%
 
| A randomly drawn scrabble tile beats a D6 die roll
 
| A randomly drawn scrabble tile beats a D6 die roll
−
| {{w|Scrabble}} is a game in which you place lettered tiles to form words. Most of the scores per letter are 1, making it rare to beat a d6. The odds are (70/100)(0) + (7/100)(1/6) + (8/100)(2/6) + (10/100)(3/6) + (1/100)(4/6) + (4/100)(6/6) ≈ 14%.
+
| {{w|Scrabble}} is a game in which you place lettered tiles to form words. Most of the scores per letter are 1, making it rare to beat a d6. The odds are (70/100)(0) + (7/100)(1/6) + (8/100)(2/6) + (10/100)(3/6) + (1/100)(4/6) + (4/100)(6/6) ≈ 14% .
 
|-
 
|-
 
| 15%
 
| 15%
Line 161: Line 155:
 
| 16%
 
| 16%
 
| Steph Curry gets two free throws but makes only one
 
| Steph Curry gets two free throws but makes only one
−
| Steph Curry's free throw percentage is 91%, so (0.91)(0.09) = 8.19% . However, the order of these is irrelevant, so the total odds are 16.38% .
+
|  
 
|-
 
|-
 
| 17%
 
| 17%
Line 169: Line 163:
 
| 18%
 
| 18%
 
| A D6 beats or ties a D20
 
| A D6 beats or ties a D20
−
| The odds are (1 + 2 + 3 + 4 + 5 + 6)/(120) = 17.5% .
+
| The odds are (1 + 2 + 3 + 4 + 5 + 6)/(120) ≈ 18% .
 
|-
 
|-
 
| 19%
 
| 19%
Line 177: Line 171:
 
| 20%
 
| 20%
 
| You get a dozen M&Ms and none of them are brown
 
| You get a dozen M&Ms and none of them are brown
−
| Depending on the source of one's M&Ms in the U.S., the proportion of browns is either 0.124 or 0.125 .  (1 - 0.125)^12 ≈ 20.1%; (1 - 0.124)^12 ≈ 20.4% .
+
|
 
|-
 
|-
 
| 21%
 
| 21%
 
| {{w|St. Louis}} has a white Christmas
 
| {{w|St. Louis}} has a white Christmas
−
| According to Randall's source, the probability of snow cover in St. Louis is 21%.
+
|
 
|-
 
|-
 
| 22%
 
| 22%
 
| An NBA team wins when they're down 10 at halftime
 
| An NBA team wins when they're down 10 at halftime
−
| Entering Q2, 0:00, and -10 into the NBA Win Probability Calculator yields 22.3% or 22.5% .
+
|
 
|-
 
|-
 
| rowspan="2"| 23%
 
| rowspan="2"| 23%
 
| You get an M&M and it's blue
 
| You get an M&M and it's blue
−
| Depending on the source of one's M&Ms in the U.S., the proportion of blues is either 0.207 or 0.25 .
+
|
 
|-
 
|-
 
| You share a birthday with a US senator
 
| You share a birthday with a US senator
−
| There are 100 Senators, but 31 Senators share 15 birthdays and 69 Senators have unique birthdays, so there are a total of 84 days of the year that are the birthday of a Senator.
+
|
 
|-
 
|-
 
| 24%
 
| 24%
 
| You correctly guess that someone was born in the winter
 
| You correctly guess that someone was born in the winter
−
| By date, the cited U.S. census data gives that 24,545,230 of the 101,909,161 people were born in the ''meteorological'' winter (December through February), or 24.09%.
+
| The winter lasts ~24% of the year, so ~24% of birthdays are in the winter.
 
|-
 
|-
 
| rowspan="2"| 25%
 
| rowspan="2"| 25%
 
| You correctly guess that someone was born in the fall
 
| You correctly guess that someone was born in the fall
−
| By date, the cited U.S. census data gives that 25,701,366 of the 101,909,161 people were born in the ''meteorological'' fall (September through November), or 25.22%.
+
| The fall lasts ~25% of the year, so ~25% of birthdays are in the fall. This statement would also have been true for spring.
 
|-
 
|-
 
| You roll two plain M&Ms and get M and M.
 
| You roll two plain M&Ms and get M and M.
−
| An M&M can land on one of two sides, one with an M and one without. The odds of "rolling" two Ms is 1/4 = 25%. The term "rolling" is used jokingly in reference to the d6s and d20s above, suggesting that an M&M is a standard d2; this becomes especially true once you consider that a more accurate reference would have been to a coin, not a die.
+
| An M&M can land on one of two sides, one with an M and one without. The odds of "rolling" two Ms is 1/4 = 25%. The term "rolling" is used jokingly in reference to the d6s and d20s above, suggesting that an M&M is a standard d2; this becomes especially true once you consider that a more accurate reference would have been two a coin, not a die.
 
|-
 
|-
 
| 26%
 
| 26%
 
| You correctly guess someone was born in the summer
 
| You correctly guess someone was born in the summer
−
| By date, the cited U.S. census data gives that 26,475,119 of the 101,909,161 people were born in the ''meteorological'' summer (June through August), or 25.98%.
+
| The summer lasts ~26% of the year, so ~26% of birthdays are in the summer.
 
|-
 
|-
 
| 27%
 
| 27%
 
| LeBron James misses a free throw
 
| LeBron James misses a free throw
−
| James' career free throw percentage is 73%, so the probability of missing is 27%.
+
|
 
|-
 
|-
 
| 32%
 
| 32%
 
| {{w|Pittsburgh}} has a white Christmas
 
| {{w|Pittsburgh}} has a white Christmas
−
| According to Randall's source, the probability of snow cover in Pittsburgh is 32%.
+
|
 
|-
 
|-
 
| rowspan="3"| 33%
 
| rowspan="3"| 33%
 
| A randomly chosen Star Wars movie (Episodes I-IX) has "of the" in the title
 
| A randomly chosen Star Wars movie (Episodes I-IX) has "of the" in the title
−
| The movies that have "of the" in their titles are Episodes II (Attack of the Clones), III (Revenge of the Sith), and VI (Return of the Jedi). This gives the odds of 3/9 ≈ 33%.
+
| Episodes II (Attack of the Clones), III (Revenge of the Sith), and VI (Return of the Jedi) are the movies. This gives the odds of 3/9 ≈ 33% .
 
|-
 
|-
 
| You win the Monty Hall sports car by picking a door and refusing to switch
 
| You win the Monty Hall sports car by picking a door and refusing to switch
Line 237: Line 231:
 
| 39%
 
| 39%
 
| LeBron James gets two free throws but misses one
 
| LeBron James gets two free throws but misses one
−
| LeBron James' free throw percentage is 73% , so the odds are (0.73)(0.27) = 19.71% . However, the order is irrelevant, so the odds are actually twice, or 39.42% .
+
|  
 
|-
 
|-
 
| 40%
 
| 40%
Line 249: Line 243:
 
| rowspan="2"|48%
 
| rowspan="2"|48%
 
| {{w|Milwaukee}} has a white Christmas
 
| {{w|Milwaukee}} has a white Christmas
−
| According to Randall's source, the probability of snow cover in Milwaukee is 48%.
+
|
 
|-
 
|-
 
| A random Scrabble tile is a letter in Carly Rae Jepsen
 
| A random Scrabble tile is a letter in Carly Rae Jepsen
Line 256: Line 250:
 
| 50%
 
| 50%
 
| You get heads in a coin toss
 
| You get heads in a coin toss
−
| There are two options in a coin toss, heads or tails, so the odds of getting heads is 50% (1/2).  Uncharacteristically for Randall, this ignores the minuscule possibility that the coin might land on its edge.
+
| There are two options in a coin toss, heads or tails, so the odds of getting heads is 50% (1/2).
 
|-
 
|-
 
| 53%
 
| 53%
 
| {{w|Salt Lake City}} has a white Christmas
 
| {{w|Salt Lake City}} has a white Christmas
−
| According to Randall's source, the probability of snow cover in Salt Lake City is 53%.
+
|
 
|-
 
|-
 
| 54%
 
| 54%
 
| LeBron James gets two free throws and makes both
 
| LeBron James gets two free throws and makes both
−
| James' career free throw percentage is 73%, so the probability of making 2 free throws is (73%)<sup>2</sup> = 53.9%.
+
|
 
|-
 
|-
 
| 58%
 
| 58%
 
| A random Scrabble tile is a letter in "Nate Silver"
 
| A random Scrabble tile is a letter in "Nate Silver"
−
| {{w|Nate Silver}} is a recurring person on xkcd. The odds of a Scrabble tile being in his name are (6 + 9 + 6 + 12 + 4 + 9 + 4 + 2 + 6)/100 = 58% . <!-- explain where these numbers come from -->
+
| {{w|Nate Silver}} is a recurring person on xkcd. The odds of a Scrabble tile being in his name are (6 + 9 + 6 + 12 + 4 + 9 + 4 + 2 + 6)/100 = 58% .
 
|-
 
|-
 
| 60%
 
| 60%
 
| You get two M&Ms and neither is blue
 
| You get two M&Ms and neither is blue
−
| Depending on the source of one's M&Ms in the U.S., the proportion of blues is either 0.207 or 0.25 .  (1 - 0.207)^2 ≈ 62.9%; (1 - 0.25)^2 ≈ 56.3%.
+
|
 
|-
 
|-
 
| 65%
 
| 65%
 
| {{w|Burlington, Vermont}} has a white Christmas
 
| {{w|Burlington, Vermont}} has a white Christmas
−
| According to Randall's source, the probability of snow cover in Burlington is 65%.
+
|
 
|-
 
|-
 
| 66%
 
| 66%
Line 296: Line 290:
 
| 73%
 
| 73%
 
| LeBron James makes a free throw
 
| LeBron James makes a free throw
−
| This is James' career free throw percentage, 73%.
+
|
 
|-
 
|-
 
| 75%
 
| 75%
Line 304: Line 298:
 
| 76%
 
| 76%
 
| You get two M&Ms and neither is red
 
| You get two M&Ms and neither is red
−
| Depending on the source of one's M&Ms in the U.S., the proportion of reds is either 0.131 or 0.125 .  (1 - 0.131)^2 ≈ 75.5%; (1 - .125)^2 ≈ 76.6%.
+
|  
 
|-
 
|-
 
| 77%
 
| 77%
 
| You get an an M&M and it's not blue
 
| You get an an M&M and it's not blue
−
| Depending on the source of one's M&Ms in the U.S., the proportion of blues is either 0.207 or 0.25 .  (1 - 0.207) = 79.3%; (1 - 0.25) = 75.0%.
+
|
 
|-
 
|-
 
| 78%
 
| 78%
 
| An NBA team wins when they're up 10 at halftime
 
| An NBA team wins when they're up 10 at halftime
−
| Entering Q2, 0:00, and 10 into the NBA Win Probability Calculator yields 77.5% or 77.7% .
+
|
 
|-
 
|-
 
| 79%
 
| 79%
 
| St. Louis doesn't have a white Christmas
 
| St. Louis doesn't have a white Christmas
−
| According to Randall's source, the probability of snow cover in St. Louis is 21%, thus the probability of ''no'' snow cover is 79%.
+
|
 
|-
 
|-
 
| 81%
 
| 81%
 
| Two random people are both right-handed
 
| Two random people are both right-handed
−
| The probability of 1 person being right-handed is about 90%, thus the probability of 2 right-handers is (90%)<sup>2</sup> = 81%.
+
|
 
|-
 
|-
 
| 83%
 
| 83%
 
| Steph Curry gets two free throws and makes both
 
| Steph Curry gets two free throws and makes both
−
| Curry's career free throw percentage is 91%, so the probability of making 2 free throws is (91%)<sup>2</sup> = 82.81%.
+
|
 
|-
 
|-
 
| 85%
 
| 85%
Line 332: Line 326:
 
| rowspan="2"| 87%
 
| rowspan="2"| 87%
 
| An NBA team up by 10 going into the 4<sup>th</sup> quarter wins
 
| An NBA team up by 10 going into the 4<sup>th</sup> quarter wins
−
| Entering Q3, 0:00, and 10 into the NBA Win Probability Calculator yields 87.2% or 87.4% .
+
|
 
|-
 
|-
 
| Someone fails to guess your card given 7 tries
 
| Someone fails to guess your card given 7 tries
−
|Assuming they guess seven different cards, there are 45 unguessed cards left. 45/52 = 0.865384615 ~ 86.5%
+
|
 
|-
 
|-
 
| 88%
 
| 88%
 
| A randomly chosen American lives outside California
 
| A randomly chosen American lives outside California
−
| This is the opposite of the previous California probability. As the probability of an American living in California is 12%, the opposite would be 88%.
+
|
 
|-
 
|-
 
| 89%
 
| 89%
 
| You roll a 3 or higher given two tries
 
| You roll a 3 or higher given two tries
−
| The probability of rolling a 3 or higher (on a 6-sided die) is 66%, so the percentage of rolling a 3 or higher given 2 tries is 1 - (1-.66)<sup>2</sup> = 89%.
+
|
 
|-
 
|-
 
| 90%
 
| 90%
Line 351: Line 345:
 
| rowspan="2"| 91%
 
| rowspan="2"| 91%
 
| You incorrectly guess that someone was born in August
 
| You incorrectly guess that someone was born in August
−
| If the odds of someone being born in August are ~9% , then the odds that a person was not born in August are ~91%. (In an average month, 8 1/3% of the population was born.  August has an above average number of days, but still only about 8.5% of the year is in August.)
+
| The odds of someone being born in August are ~9% , so the odds that a person was not born in August is ~91% .
 
|-
 
|-
 
| Steph Curry makes a free throw
 
| Steph Curry makes a free throw
−
| This is Curry's career free throw percentage, 91%.
+
|
 
|-
 
|-
 
| 92%
 
| 92%
 
| You guess someone's birth month at random and are wrong
 
| You guess someone's birth month at random and are wrong
−
| On average, a month lasts 8⅓% of the year. Thus, if you were to guess someone's birth month at random, you would be wrong 91 ⅔% of the time.
+
| On average, a month lasts ~8% of the year. Thus, if you were to guess someone's birth month at random, you would be wrong ~92% of the time.
 
|-
 
|-
 
| 93%
 
| 93%
 
| Lebron James makes a free throw given two tries
 
| Lebron James makes a free throw given two tries
−
| James' career free throw percentage is 73%, so the percentage of his making at least 1 free throw given 2 tries is 1 - (1-.73)<sup>2</sup> = 93%.
+
|
 
|-
 
|-
 
| 94%
 
| 94%
Line 370: Line 364:
 
| 95%
 
| 95%
 
| An NBA team wins when they're up 20 at halftime
 
| An NBA team wins when they're up 20 at halftime
−
| Entering Q2, 0:00, and 20 into the NBA Win Probability Calculator yields 94.7% or 94.8% .
+
|
 
|-
 
|-
 
| 96%
 
| 96%
Line 382: Line 376:
 
| 98%
 
| 98%
 
| You incorrectly guess someone's birthday is this week
 
| You incorrectly guess someone's birthday is this week
−
| The odds of this happening are about 51/52 ≈ 98%. (This depends on the week; there are more births in early October and fewer in holiday weeks.)
+
| The odds of this happening are about 51.14/52.14 ≈ 98% .
 
|-
 
|-
 
| 98.5%
 
| 98.5%
 
| An NBA team up 15 points with 8 minutes left wins
 
| An NBA team up 15 points with 8 minutes left wins
−
| Entering Q4, 8:00, and 15 into the NBA Win Probability Calculator yields 98.0% or 98.6% .
+
|
 
|-
 
|-
 
| 99%
 
| 99%
 
| Steph Curry makes a free throw given two tries
 
| Steph Curry makes a free throw given two tries
−
| James' career FT percentage is 91%, so the percentage of his making at least 1 FT given 2 tries is 1 - (1-.91)<sup>2</sup> = 99%.
+
|
 
|-
 
|-
 
| 99.5%
 
| 99.5%
 
| An NBA team that's up by 30 points at halftime wins
 
| An NBA team that's up by 30 points at halftime wins
−
| Entering Q2, 0:00, and 30 into the NBA Win Probability Calculator yields 99.4% .
+
|
 
|-
 
|-
 
| 99.7%
 
| 99.7%
 
| You guess someone's birthday at random and are wrong
 
| You guess someone's birthday at random and are wrong
−
| The odds of this are 364/365 ≈ 99.7%.
+
| The odds of this are 364.25/365.25 ≈ 99.7% .
 
|-
 
|-
 
| 99.8%
 
| 99.8%
Line 406: Line 400:
 
| 99.9%
 
| 99.9%
 
| A random group of three people contains a right-hander
 
| A random group of three people contains a right-hander
−
| About 90% of people are right-handed, so the percentage of at least 1 right-hander in a group of 3 is 1 - (1-.9)<sup>3</sup> = 99.9%.
+
|
 
|-
 
|-
 
| 99.99%
 
| 99.99%
 
| You incorrectly guess the last four digits of someone's social security number
 
| You incorrectly guess the last four digits of someone's social security number
−
| There are nine digits in a Social Security Number, but the last four are commonly used as an identity verification factor. The odds of this are 1 - (1/10)<sup>4</sup> = 99.99% .
+
| The odds of this are 1 - (1/10)<sup>4</sup> = 99.99% .
 
|-
 
|-
 
| 99.9999999999999995%
 
| 99.9999999999999995%
 
| You pick up a phone, dial a random 10-digit number, and say 'Hello Barack Obama, there's just been a {{w|Moment magnitude scale|magnitude}} 8 earthquake in {{w|California}}!" and are wrong
 
| You pick up a phone, dial a random 10-digit number, and say 'Hello Barack Obama, there's just been a {{w|Moment magnitude scale|magnitude}} 8 earthquake in {{w|California}}!" and are wrong
−
| This probability combines two events.
+
|
−
 
 
−
First, the probability that a random 10-digit telephone number belongs to Obama is 1/10<sup>10</sup>. This ignores potential complications from Obama owning multiple phones or failing to answer personally (perhaps using an assistant or answering machine). Additionally, it assumes numbers are dialed at random rather than making more intelligent guesses, such as using likely addresses to guess area codes.
 
−
 
 
−
Second, the probability of a magnitude 8 California quake is given in a previous entry as 0.2% per year. Although the time window for an earthquake to "just occur" is not given, a 15 minute window corresponds (within rounding error) to the total probability given.
 
 
|-
 
|-
 
| 0.00000001%
 
| 0.00000001%
 
| You add "Hang on, this is big — I'm going to loop in Carly Rae Jepsen", dial another random 10-digit number, and she picks up
 
| You add "Hang on, this is big — I'm going to loop in Carly Rae Jepsen", dial another random 10-digit number, and she picks up
−
| Carly Rae Jepsen is a Canadian singer. As Canada uses the 10-digit {{w|North American Numbering Plan}}, the odds of a random number being hers would be (1/10)<sup>10</sup> = 0.00000001%. Like Obama, this ignores the possibility that she has multiple phones or that she doesn't answer personally.
+
| The odds of this are 1 - (1/10)<sup>10</sup> = 0.00000001% .
 
|}
 
|}
 +
 +
 +
===References===
 +
{{#tag:references}}
  
 
==Trivia==
 
==Trivia==
−
* In the original comic, "outside" in the 88% probability section is spelled incorrectly as "outide". In addition, the 39% section had "two free throw" instead of "throws".
+
In the original comic, "outside" in the 88% probability section is spelled incorrectly as "outide". In addition, the 39% section had "two free throw" instead of "throws".
−
 
 
−
* The (seemingly unimportant) odds of LeBron James' versus Stephen Curry's free throws and names in Scrabble refer to [[2002: LeBron James and Stephen Curry]].
 
  
−
* If you were to act out all the M&M-related probabilities, you would draw (or flip) 32 M&Ms in total. In addition, you would draw 8 Scrabble tiles in total for each Scrabble-related probability.
+
The (seemingly unimportant) odds of LeBron James' versus Stephen Curry's free throws and names in Scrabble refer to [[2002: LeBron James and Stephen Curry]].
  
 
==Transcript==
 
==Transcript==
−
[Large heading, centered.]
+
Probability Comparisons
−
 
 
−
<big>Probability Comparisons</big>
 
−
 
 
−
[Left column.]
 
  
 
0.01% You guess the last four digits of someone's social security number on the first try
 
0.01% You guess the last four digits of someone's social security number on the first try
Line 546: Line 534:
  
 
35% A random Scrabble tile is one of the letters in "random"
 
35% A random Scrabble tile is one of the letters in "random"
−
 
−
[Right column.]
 
  
 
39% LeBron James gets two free throws but misses one
 
39% LeBron James gets two free throws but misses one
Line 641: Line 627:
 
0.00000001% You add "Hang on, this is big — I'm going to loop in Carly Rae Jepsen", dial another random 10-digit number, and she picks up
 
0.00000001% You add "Hang on, this is big — I'm going to loop in Carly Rae Jepsen", dial another random 10-digit number, and she picks up
  
−
[In light grey color and in the lower left corner there is text.]
+
'''PROBABILITY COMPARISONS'''
−
 
 
−
Sources: https://xkcd.com/2379/sources/
 
−
 
 
−
==References==
 
−
<references/>
 
  
 
{{comic discussion}}
 
{{comic discussion}}
 
[[Category:Statistics]]
 
[[Category:Statistics]]
 
[[Category:Comics featuring real people]]
 
[[Category:Comics featuring real people]]
−
[[Category:Comics featuring politicians]]
 
−
[[Category:Comics featuring Nate Silver]]
 
−
[[Category:Basketball]]
 
−
[[Category:Christmas]]
 
−
[[Category:Food]]
 

Please note that all contributions to explain xkcd may be edited, altered, or removed by other contributors. If you do not want your writing to be edited mercilessly, then do not submit it here.
You are also promising us that you wrote this yourself, or copied it from a public domain or similar free resource (see explain xkcd:Copyrights for details). Do not submit copyrighted work without permission!

To protect the wiki against automated edit spam, we kindly ask you to solve the following CAPTCHA:

Cancel | Editing help (opens in new window)

Templates used on this page:

Retrieved from "https://www.explainxkcd.com/wiki/index.php/2379:_Probability_Comparisons"