Question

Amy’s birthday is on December 6. What is the probability that at least one of the 40 other students has the same birthday as Amy? (Provide a numerical expression, but don’t attempt to simplify. Assume there are 365 days in every year.)

Answer 1

An entertaining example is to determine the probability that in a randomly selected group of n people at least two have the same birthday. If one assumes for simplicity that a year contains 365 days and that each day is equally likely to be the birthday of a randomly selected person, then in a group of n people there are 365ⁿ possible combinations of birthdays. The simplest solution is to determine the probability of no matching birthdays and then subtract this probability from 1. Thus, for no matches, the first person may have any of the 365 days for his birthday, the second any of the remaining 364 days for his birthday, the third any of the remaining 363 days, and the nth any of the remaining 365 - n + 1. The number of ways that all n people can have different birthdays is then 365*364*........* (365 - n + 1) ,so that the probability that at least two have the same birthday is:

here n=41 (total students).

This is required expression to get the desired result.

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