Hello, Malicant!

Welcome aboard!

The problem is to design a program that can work out

how many people need to be in a room for the probability of 2 people

sharing the same birthday to be greater than 0.5.

If there are two people in a room, the probability of them

. . sharing the same birthday would be 1/365. . . . . Yes!

If there were 3 people then the probability would be 2/365. . . . . no

With 3 people, look at the opposite probability:no oneshares a birthday.

The first person can have any birthday:

The second must have a different birthday:

The third must have yet another birthday:

Hence: .

Therefore: .

We want people to share (at least) a birthday with probability greater than 0.5

The probability thatnoneof them have the same birthday is:

. .

When this product dropsbelow0.5, we've found it!

I trust you can write the program now . . .