SOLUTION: A group of five people are selected at random. What is the probability that at least two of them were born on the same day of the week? (Assume that a person is equally likely to b
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Question 1201521: A group of five people are selected at random. What is the probability that at least two of them were born on the same day of the week? (Assume that a person is equally likely to be born on any day of the week. Round your answer to four decimal places) Found 2 solutions by ikleyn, greenestamps:Answer by ikleyn(52864) (Show Source):
The opposite of at least two of them having been born on the same day of the week is all of them having been born on different days. So calculate the probability that five people will have been born on different days of the week and the take the complement.
Probably the easiest way to calculate the probability of 5 people having been born on different days of the week is to look at the people one at a time and see the probabilities that each one was born on a different day than the others.
The first person could have been born on any day of the week; the probability is 7/7 = 1.
The second person could have been born on any of the 6 remaining days of the week; that probability is 6/7.
The third person could have been born on any of the 5 remaining days of the week; that probability is 5/7.
The fourth person could have been born on any of the 4 remaining days of the week; that probability is 4/7.
The fifth person could have been born on any of the 3 remaining days of the week; that probability is 3/7.
The probability that they all were born on different days of the week is then
(7/7)(6/7)(5/7)(4/7)(3/7) = 360/2401
So the probability that at least 2 of them were born on the same day of the week is
