# The "birthday problem" in probability theory

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?

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#### Solution Preview

a) For any value of n, the desired probability can be found by first finding the probability that all n of the birthdays are different (see attached Word document and Excel worksheet for calculation details). From this we can ...

#### Solution Summary

This problem shows how use Excel to solve the "birthday problem", the probability that, in a set of n randomly chosen people, some pair of them will have the same birthday.