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# Analytical Estimate

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a. In a class roster of 18 students, what are the chances that there are at least 2 people with the same birthday (same day, not same year)? Given a birthday of July 29th, please provide a detailed analytical estimate of the likelihood that this will happen.

b. A street performer approaches you to make a bet. He shows you three cards: one that is blue on both sides, one that is orange on both sides, and one that is blue on one side and orange on the other. He puts the cards in the bag, pulls out one, and puts it on the table. Both of you can see that the card is blue on top, but haven't seen the other side. The street performer bets you \$50 that the other side of the card is also blue. Should you take the bet and why?

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#### Solution Preview

Please refer to the attachment for part a.

b)
No, we should not take this bet. If we see a blue side then we know that it's not the 2-sided orange card. But from the two remaining cards that could be on the table, there are actually 3 different ways to see ...

#### Solution Summary

An analytical estimate is examined.

\$2.19