w-birthday - Appendix A The Birthday Problem The setting is...

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Appendix A The Birthday Problem The setting is that we have q balls. View them as numbered, 1 , . . . , q . We also have N bins, where N q . We throw the balls at random into the bins, one by one, beginning with ball 1. At random means that each ball is equally likely to land in any of the N bins, and the probabilities for all the balls are independent. A collision is said to occur if some bin ends up containing at least two balls. We are interested in C ( N, q ), the probability of a collision. The birthday paradox is the case where N = 365. We are asking what is the chance that, in a group of q people, there are two people with the same birthday, assuming birthdays are randomly and independently distributed over the days of the year. It turns out that when q hits 365 the chance of a birthday collision is already quite high, around 1 / 2. This fact can seem surprising when Frst heard. The reason it is true is that the collision probability C ( N, q
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w-birthday - Appendix A The Birthday Problem The setting is...

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