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 1101847: 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.) Found 2 solutions by math_helper, ikleyn:Answer by math_helper(2461) (Show Source):
You can put this solution on YOUR website! Let A be the event that at least two justices have the same birthday.
P(A) = 1 - P(A')
—
P(A') = (364/365)*(363/365)*(362/365)*(361/365)*(360/365)*(359/365)*(358/365)*(357/365)
P(A') = (364*363*362*361*360*359*358*357)/(365^8)
P(A') = 0.9053762
—
P(A) = 1-0.9053762 = 0.0946238, rounded to 4 decimal places: 0.0946
The full space of events is the set of all records of the length 9; each the record contains 9 numbers:
one number from 1 to 365 (the birthday) in each position from 1 to 9.
The full set contains records/elements.
The complement set consists of those records that have no two equal numbers in all 9 positions (no repetition allowed)
1) we can select any of 365 numbers in the 1-st position,
2) we can select any of the remaining 364 numbers in the 2-nd position,
. . .
and so on . . . till
. . .
8) we can select any of the remaining 358 numbers in the 8-th position,
9) we can select any of the remaining 357 numbers in the 9-th position.
In all, the complementary set has 365*364*363*362*361*360*359*358*357 records/elements.
Therefore, the probability under the question is - = 0.0946.
