12. Airlines sometimes overbook ights. Suppose that for a plane with 50 seats, 55 passengers have tickets.

Question:

De ne the random variable Y as the number of ticketed passengers who actually show up for the ight.

The probability mass function of Y appears in the accompanying table.

y 45 46 47 48 49 50 51 52 53 54 55 p(y) .05 .10 .12 .14 .25 .17 .06 .05 .03 .02 .01

a. What is the probability that the ight will accommodate all ticketed passengers who show up?

b. What is the probability that not all ticketed passengers who show up can be accommodated?

c. If you are the rst person on the standby list

(which means you will be the rst one to get on the plane if there are any seats available after all ticketed passengers have been accommodated), what is the probability that you will be able to take the ight? What is this probability if you are the third person on the standby list?

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Question Posted: Sep 10, 2024 12:02 PM

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