# 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

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) â‰ˆ 1 âˆ’ exp(âˆ’(30C3)/365^2) = 0.0300

Option (A) is correct.

Quiz of this Question

Level Up Your GATE Prep!
Embark on a transformative journey towards GATE success by choosing Data Science & AI as your second paper choice with our specialized course. If you find yourself lost in the vast landscape of the GATE syllabus, our program is the compass you need.

Previous
Next