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Airlines sometimes overbook flights. Suppose that for a plane with 50 seats, 55 passengers have tickets. Define the random variable $Y$ as the number of ticketed passengers who actually show up for the flight. The probability mass function of $Y$ appears in the accompanying table.(a) What is the probability that the flight 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 first person on the standby list (which means you will be the first 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 flight? What is this probability if you are the third person on the standby list?

(a) 0.83 $\\$ (b) 0.17$\\$(c) 0.66

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Video Transcript

Okay. So for sea parts, eh? 12 were asked what probability that the flight will be a cop will accommodate all ticketed passengers who show up what that means. Let's go back. Next pee accommodates, um off. If the passengers sort of left center, it was 2 50 if you saw him about about less than or equal to date up. Since he quit. 2.83 now for part B. We're us. Uh, see your ass. What is the probability that not all ticketed passengers who show up can be accommodated? You know that there's 55 passengers who have tickets and only 56. So that's this. He were Why? It's good. Yeah, they used me. Plus quick five plus 50.3 plus 0.2 plus one. You could 10.17. Okay. Now, where parts see were asked, if you are the first person on the standby list, what is the probability that you will be able to succeed? But that means that there's 50 people already seated p or not 50. There's only 49 people said seated, and there's one more seat remaining. So that's just why it's less than or equal to 49 which is equal to 0.66 and in the same for three. So that's why it's less than equal to 47 but some things to point to something.

University of California, Berkeley