Question

What is the probability that in a room of n people, at least three of them have the same birthday? Explain all the terms in your solution.

What is the fewest amount of people such that the probability of at least three of these people having the same birthday is greater than 1/3? You will have to code your solution from the first question and plug in values for n. Include the code snipped you used to solve this.

Answer 1

Obviously if n>366, the answer is 100% since there are not enough days in the year for everyone to have a different birthday. Otherwise, ignoring the fact that February 29 occurs only about 25% as often as the other dates, and fact that distribution of birthday is not in real life uniform, I think mainly because a lot of wants to be June brides so many people are born in March,assuming the distribution is uniform over 365 days and nobody is born on Sadie Hawkins day, the way that is calculated is to compute the probability that all the birthday are different, and then subtract from 1. That works out to 364/365, (the probability that the second person’s birthday is different from the first ) times 363/365 (the probability that the third birthday is different from the first two assuming the first 2 are different) etc. I obviously can’t carry out the calculation since I don’t know what is n is. But my recollection is it turns out that the probability is at least 1/2 if n is around 50 ,or maybe less than 50. Thank you......