Before you tell me that I need professional help, let me tell you I have gone that route. You talk about your problems and they call you a narcissist. I tell them to go look yourself in the mirror. They give their meanest clients jobs as debt collectors. You have to be crazy to go back again and again to see one of them.
For two people, the probability is 1/365. Three people represent three combinations of two people, so the probability is 1/365 + 1/365 + 1/365 = 1/122. Four people give 6 two-person combinations = 6/365 = 1/61.
In order to be probable, ie. have a probability of 1/2 or greater, we need a number whose combinations add up to 365/2 = 182. Twenty people give 190 two-person combinations, giving a probability that two of those twenty people share a birthday of just over 50%.
