SOLUTION: What is the probability that 2 (or more) people in a random group of 25 people have a common birthday? (This is the famous Birthday Paradox Problem.)

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Question 385347: What is the probability that 2 (or more) people in a random group of 25 people have a common birthday? (This is the famous Birthday Paradox Problem.)
Answer by sudhanshu_kmr(1152) About Me  (Show Source):
You can put this solution on YOUR website!

Here we firstly find the probability of event when all 25 people have different birthday...
probability of first people have its own birthday = 365/365 ( sure )
probability of second people have different b'day to first = 364/365

probability of third people have different b'day to first and second = 363/365
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similarly for 25th person, probability of different b'day = 341/365

probability when all have different b'day P(A) = 365/365 * 364/365 *.....*341/365

= (1/365)^24 * ( 364 *.....*341)

now, probability that 2 or more people have common b'day = P(A')

= 1-P(A)