Brooks Adam Doyle Hotel: A new hotel, Brooks Adam Doyle Hotel (Or simply BAD Hotel) opens up with 100 identical rooms and is booked fully on the first night. We can index the customers with index i = 1, 2, . . . , 100. When the first customer came, the absent-minded receptionist Hilbert randomly gave him one of the keys (with equal probability). His supervisor scolded him and for the rest of the people i = 2, 3, . . . , 100 he gave the keys properly if he already gave the key of Customer i to someone else, he chooses a random person's key uniformly from the remaining keys otherwise he gives the proper key. (a) Suppose that he gives people i = 4 . . . 100 their own key. What is the probability that he gave Customer 2 her own key? (b) What is the probability that customer 3 doesn't get her own key? (c) What is the probability that customer 3 gets her own key.
Brooks Adam Doyle Hotel: A new hotel, Brooks Adam Doyle Hotel (Or simply BAD Hotel) opens up with 100 identical rooms and is booked fully on the first night. We can index the customers with index i = 1, 2, . . . , 100. When the first customer came, the absent-minded receptionist Hilbert randomly gave him one of the keys (with equal
(a) Suppose that he gives people i = 4 . . . 100 their own key. What is the probability that he gave Customer 2 her own key?
(b) What is the probability that customer 3 doesn't get her own key?
(c) What is the probability that customer 3 gets her own key.
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