Question

what is the probability of 2 friends having different birthdays​

Answer 1

Answer:

Explanation:

The second person's birthday has to be different. There are 364 different days to choose from, so the chance that two people have different birthdays is 364/365.

Here's how you can find the solution:

Let the probability of two friends having their birthdays on any one day of the year be P.

The probability of the 1st friend having the birthday on any day of the year would be a sure event, P1= 365/365

The probability of the 2nd friend having the birthday on the same day as 1st friend’s, P2= 1/365

The probability of both the events happening simultaneously would be, P= P1 * P2 = 1/365

Hence, the probability of them having different birth dates (P’) = 1–(1/365) = 364/365

But, consider the case where the problem is to find the probability of two friends having their birthday on a given day of the year (say 21st January)

Here. the probability of the 1st friend having the birthday on 21st Jan (P1)= 1/365

The probability of the 2nd friend having the birthday on the same day as 1st friend’s birthday (P2)= 1/365

So, the probability of them having the birthday on the same day (P) = P1 * P2 = (1/365)*(1/365) = (1/365)^2

The Probability of them having different birth dates (P’) = 1–(1/365)^2