In a gathering of 15 person none of them was born in a leap year. find the probability that at least two have birthday on same date.

Solution (By Examveda Team)

First we would find the probability of birth day on different dates.
There are 15 peoples, so,

There are 15 peoples therefore,
Probability of different birthday = (365 *364*363* ....... * 351)/(365¹⁵)

Probability of different birthday = 365!/(365-15)! *365¹⁵)
Then,
The probability of same date = 1 - probability of different dates
The probability of same date =1 - [365!/(365-15)!] *365¹⁵)
The probability of same date,
= (350!*365¹⁵ - 365!)/365¹⁵.