## (Solution document) Be honest, have you ever met someone, only to be shocked that you share the same birthday?

Be honest, have you ever met someone, only to be shocked that you share the same birthday? We have all been there at one point or another. In this week's discussion, you will be asked to address this event with a measure of probability.

See, each semester I ask each of my classes of about 32 face-to-face students the question, "What do you believe the probability is that there exists a common birthday(s) among those in this class?" After each person has the opportunity to consult his or her neighbor, I proceed to write down the guesses on the board. Those guesses often look something like this: 1%, 10%, 25%,50%, 67%, 90% 100%. As we all know, only one of these can be correct (if any).

Using your understanding of counting techniques and probability, investigate the answer to this question. What do you calculate to be the true probability of such an event? Provide any and all reasoning.

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