Suppose 40 people are in a room. What is the probability that none of them share a birthday?

Question

Suppose 40 people are in a room. What is the probability that none of them share a birthday?

Answer 1

Let's assign a different birthday to each of 40 people: ₃₆₅C₄₀ = a.

P(all different) =a/365⁴⁰ = b.

P(not all different birthdays) = 1 - b.

 

Assumes 365 days per year.