Determine the probability that at least 2 people in a room of 14 people share th

Question

Determine the probability that at least 2 people in a room of 14 people share the same birthday, ignoring leap years and assuming each birthday is equaily lkoly, by answering the following questions (a) Compute the probability that 14 people have different birthdays b) The complement of "14 people have dfferent birthdays is at least 2 share a birthday (a) The probability that 14 people have different birthdays«O Use this information to compute the probabilty that at least 2 people out of 14 share the same bithday Round to four decimal places as needed ) (b) The probabiity that at least 2 people out of the 14 share a birthday is Round to four decimal places as needed)

Explanation / Answer

Solution:-
1) probability = 365P14/365^14
= 578713774595928503846356381667328000/365^14
= 0.7769

2) P(X >= 2) = 1 - 0.7769 = 0.2231

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