Mathematics, 12.03.2020 06:43 austinmiller3030

There are people in line, indexed by =1,…, , to enter a theater with seats one by one. However, the first person ( =1 ) in the line is drunk. This person has lost her ticket and decides to take a random seat instead of her assigned seat. That is, the drunk person decides to take any one of the seats 1 to with equal probability. Every other person =2,…, that enters afterwards is sober and will take his assigned seat (seat ) unless his seat is already taken, in which case he will take a random seat chosen uniformly from the remaining seats. Suppose that =3 . What is the probability that person 2 takes seat 2? (Enter a fraction or a decimal accurate to at least 3 decimal places.)

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There are people in line, indexed by =1,…, , to enter a theater with seats one by one. However, th...

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