Editing 2379: Probability Comparisons

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.

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.

| There are nine digits in a {{w|Social Security Number}}, but the last four are commonly used as an identity verification factor. (1/10)⁴ = 0.0001, or 0.01%

| Depending on the source of one's M&Ms in the U.S., the proportion of reds is either 0.131 or 0.125 .  0.131^3 ≈ 0.225%; 0.125^3 ≈ 0.177% .

| 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% .

| 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 .  0.25⁴≈ 0.39%; 0.259⁴ ≈ 0.45% . Both are closer to 0.4% .

| 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%.

| 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)²... Summing all of these from 1 to 365 gives us his total odds of winning at any point in the game are ≈ 1.015% .

|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% .

| There are 52 cards in a normal deck of cards (excluding jokers), so the probability is 1/52, which is approximately 1.9%.

| The chance of correctly predicting a coin toss is 0.5, or 50%. The chance of predicting 5 in a row is 0.5⁵, or 3.125%.

| Swap out 0.73 for 0.91 in the above calculations to find Steph Curry's odds of winning. This sum yields ~3.04% .

| 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/>

| 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% .

| 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)², which is about 7%.

| 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%.

| 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%.

| 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.

| 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% .

| 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% .

| 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%.

| 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%.

| 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%.

| James' career free throw percentage is 73%, so the probability of missing is 27%.  

| 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%.

| 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% .

| 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.

| James' career free throw percentage is 73%, so the probability of making 2 free throws is (73%)² = 53.9%.

| {{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 -->

| 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%.

| This is James' career free throw percentage, 73%.

| 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%.

| 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%.

| Curry's career free throw percentage is 91%, so the probability of making 2 free throws is (91%)² = 82.81%.

| This is Curry's career free throw percentage, 91%.

| 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)² = 93%.

| 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)⁴ = 99.99% .

First, the probability that a random 10-digit telephone number belongs to Obama is 1/10¹⁰. 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.

| 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)¹⁰ = 0.00000001%. Like Obama, this ignores the possibility that she has multiple phones or that she doesn't answer personally.

* 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.