Question

Two women in a group of 25 people shared the same name and the same birthday. Discuss whether this is a surprising result. Do you think it is more likely that you will find a pair of people in a room of 25 who share a first name or a pair of people who share a birthdate?

Answer 1

For the choice of birth date, we have 365 options to choose from whereas, for the choice of name, there are uncountable choices. Hence, it is surprising that two women in a group will share the same name and the same birthdate.

As we said, for birthdate, we have only 365 choices. Number of ways in which we can select 2 women from 25

The probability that two women will not have the same birthdate

The probability that all 300 pairs of women will not have the same birthdate

The probability that 2 women will have the same birthdate

Now, for the case of name, we have a huge number of choices, much greater than 365. As these choices will keep on increasing, the probability that two women among 25 will have the same name will keep on reducing. And hence, the probability that two women will have the same name and the same birthdate will be even less. Hence, it is a surprising result that 2 women among 25 will share the same name and the same birthdate.

And it is more likely that a pair of people in a room of 25 will share the same birthdate than a pair of people sharing the same name.

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