GATE | GATE CS Mock 2018 | Question 58

What is the probability of 3 students sharing a birthday in a class of 30 students is ________ .
(A) 0.0300
(B) 0.7029
(C) 0.5604
(D) None of the above


Answer: (A)

Explanation: Imagine checking every triple and calling it a “success” if all three have the same birthdays. The total number of successes is approximately Poisson with mean value 30C3/365^2. Here 30C3 is the number of triples, and 1/365^2 is the chance that any particular triple is a success. The probability of getting at least one success is obtained from the Poisson distribution :

P( at least one triple birthday with 30 people) ≈ 1 − exp(−(30C3)/365^2) = 0.0300

Option (A) is correct.

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