Probability of Matching Birthdays (Graph)
Calculate and graph a table showing the probability that at least one pair of birthdays will match as the group size varies.
(1) Probability that none of the birthdays in a group match
(2) Probability that at least one pair of birthdays matches within a group
The probability appears high because people tend to think in terms of the probability that their own birthday will match.
This is known as the “Birthday Paradox.” Note that leap years are not taken into account.
| \(\normalsize \\ \hspace{20px}\overline{p}(n)={\large\frac{364}{365}}\times{\large\frac{363}{365}}\times{\large\frac{362}{365}}\times\cdots\\ \hspace{50px}={\large\frac{365\times364\times363\times\cdots\times(365-n+1)}{365^n}}\\ \hspace{50px}={\large\frac{365!}{365^n(365-n)!}}\\\) |
(2) Probability that at least one pair of birthdays matches within a group
| \(\normalsize\\ \hspace{20px}p(n)=1-\overline{p}(n)\\\) |
The probability appears high because people tend to think in terms of the probability that their own birthday will match.
This is known as the “Birthday Paradox.” Note that leap years are not taken into account.
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