Question

in a group of 2 ,what is probability that 2 people have same birthday

Answer 1

Answer:

Assuming you mean date and month rather than year, it’s 0.03 %. This is worked out by flipping it the other way. For example what’s the probability of me NOT sharing a birthday with anyone in an empty room? Clear the answer is 1 or 365/365, but if someone comes in and I ask the question again they have 364/365 chances of not sharing a birthday.

The calculation is 365/365 * 364/365 = 0.997 of the two of us not sharing a birthday so the balance 0.03% is us sharing a birthday (to make it add to one as they are the only the outcomes.

By the way to get a chance of better than 50% having the same birthday you need 23 people just keep multiplying the probabilities eg for person number 3 you multiply by 363/365 and so on. Hope this helps!