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# The "birthday problem" in probability theory

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One of the most famous probability calculations is called the "birthday problem". In probability theory, the birthday problem or birthday paradox concerns the probability that, in a set of n randomly chosen people, some pair of them will have the same birthday. Ignoring leap year and assuming that there are only 365 days in a year, complete the following:

a) Using Excel, find the birthday problem probabilities for all values of n from 2 to 60 inclusive.

b) Create a plot where the x-axis = number of randomly chosen people and the y-axis = probability that at least one pair of people have the same birthday.

c) How many people would have to be chosen so that the probability of at least one pair having the same birthday is greater than 0.5?

d) How many people would have to be chosen so that the probability of at least one pair having the same birthday is greater than 0.8?