what is the probability that in a group of 20 randomly selected students (from a

Question

what is the probability that in a group of 20 randomly selected students (from a current section of STA 9708 Statistics) 2 or more will be found to share the same birthday? Ignore leap years (like 2012)? what is the probability that in a group of 20 randomly selected students (from a current section of STA 9708 Statistics) 2 or more will be found to share the same birthday? Ignore leap years (like 2012)? what is the probability that in a group of 20 randomly selected students (from a current section of STA 9708 Statistics) 2 or more will be found to share the same birthday? Ignore leap years (like 2012)?

Explanation / Answer

There are 365^20 ways to choose birthdays.

There are 365P20 ways so that no two have the same birthday.

As

P(2 or more with same birthday) = 1 - P(all birthdays unique)

Then

P(2 or more with same birthday) = 1 - 365P20 / (365^20)

= 0.588561616 [ANSWER]

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