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Find the probability that among seven persons at least two were born on the same day....

Find the probability that among seven persons at least two were born on the same day. (By day I don't mean date, I mean Mon, Tues, Wed, Thurs, Fri, Sat or Sun)

Math   Statistics-And-Probability   
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Answer #1

The probability that among seven persons at least two were born on the same day = 1 - Probability that all seven persons were born on different days.

Number of ways in which all seven persons were born on different days = Number of ways of filling n = 7 blank spaces(here days) with n = 7 distinct things(here persons) such that each blank space is filled with one thing = = = 7! = 5040

Each person could be born in any of the seven days.

Therefore the total number of ways the seven persons were born on seven days =

The probability that all seven persons were born on different days = = 0.00612

Therefore the probability that among seven persons at least two were born on the same day = 1 - 0.00612 = 0.99388

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