Determine the probability that at least 2 people in a room of 8 people share the

Question

Determine the probability that at least 2 people in a room of 8 people share the same birthday, ignoring leap years and assuming each birthday is equally likely, by answering the following questions (a) Compute the probability that 8 people have different birthdays. (b) The complement of "8 people have different birthdays" is "at least 2 share a birthday". Use this information to compute the probability that at least 2 people out of 8 share the same birthday (a) The probability that 8 people have different birthdays is (Round to four decimal places as needed.) (b) The probability that at least 2 people out of the 8 share a birthday is (Round to four decimal places as needed.)

Explanation / Answer

a) There are 365 possible birthdays and these can be assigned to 8 people in

365P8 ways.

=> Probability that 8 poeple have different birthdays

= 365P8 / (365)8

= 0.9257.

(b) Probability that atleast 2 people have same birthday = 1 - 0.9257

= 0.0743.

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