SOLUTION: What is the probability that at least two of the nine justices of the U.S. Supreme Court have the same birthday? (Use a 365-day year. Round your answer to four decimal places.)

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Question 534256: What is the probability that at least two of the nine justices of the U.S. Supreme Court have the same birthday? (Use a 365-day year. Round your answer to four decimal places.)
Answer by fcabanski(1391) About Me  (Show Source):
You can put this solution on YOUR website!
The probability that one person has a unique birthday is 365/365.


The probability that the second person (justice) doesn't share the birthday with the first person is 364/365. There are 364 choices remaining once the day for the first person is removed.


Similarly, each nth person has the probability of a unique date (365-n+1)/365.


Multiply all those probabilities together:


(365*364*...357)/365^9 = 364*363*...357/365^8 (cancel the 365 in the numerator with one 365 in the denominator.


This is the probability nobody shares a birthday. It's .9054. Subtract that from 1 to find the probability that at least two share a birthday.


1-.905376 = .094623 = 9.4623 %