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# Statement of a problem № m40571

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Airlines sometimes overbook flights. Suppose that for a plane with 100 seats, an airline takes 110 reservations. Define the random variable x as x = the number of people who actually show up for a sold out flight on this plane From past experience, the probability distribution of x is given in the following table: x p(x) 95 ………………. 0.05 96 ………………. 0.10 97 ………………. 0.12 98 ………………. 0.14 99 ………………. 0.24 100………………. 0.17 101………………. 0.06 102………………. 0.04 103………………. 0.03 104………………. 0.02 105 ………………. 0.01 106 ………………. 0.005 107 ………………. 0.005 108 ………………. 0.005 109 ………………. 0.0037 110 ………………. 0.0013 a. What is the probability that the airline can accommodate everyone who shows up for the flight? b. What is the probability that not all passengers can be accommodated? c. If you are trying to get a seat on such a flight and you are number 1 on the standby list, what is the probability that you will be able to take the flight? What if you are number 3?

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