(Answered) Question there is a retired professor who used to love to

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Question: There is a retired professor who used to love to go into a probability class of thirty or more students and announce "I will give even money odds that there are two people in this classroom with the same birthday." With thirty students in the room, what is the probability that all have different birthdays? What is the minimum number of students that must be in the room so that the professor has at least probability one half of winning the bet? What is the probability that he wins his bet if there are 50 students in the room. Does this probability make sense to you? (There is no wrong answer to that question!) Explain why or why not.

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