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What is the probability that 4 randomly selected people all have different birthdays?...

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surfer3 | Valedictorian

Posted May 19, 2012 at 4:33 PM via web

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What is the probability that 4 randomly selected people all have different birthdays? Round the answer to four decimal places

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thilina-g | College Teacher | (Level 1) Educator

Posted May 19, 2012 at 5:10 PM (Answer #1)

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There are 365 out of 365 ways to select the birthday of first person. Therefore the number of ways that we can choose a birthday for second person is 364 out of 365.

Therefore the probability of two persons not having the same birthday is,

`P(2) = 365/365 xx364/365`

For four people,

`P(4) = 365/365 xx 364/365 xx 363/365 xx 362/365`

`P(4) = 0.9836`

 

Therefore the probability of 4 people having different birthdays is 0.9836

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