4. 4 points My Notes Ask Your Teacher Airlines sometimes overbook flights. Suppo

Question

4. 4 points My Notes Ask Your Teacher Airlines sometimes overbook flights. Suppose that for a plane with 50 seats, 55 passengers have tickets. Detine the random variable Y as the number of ticketed passengers who actually show up for the tlight. The probability mass function of Yappears in the accompanying table. L45 46 47 48 49 50 55 5 54-5 pty) 0.04 0.10 0.12 0.14 26 0.17 0.06 0.05 0.03 0.02 0.01 (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 avallable after all ticketed passengers have been accommodated), what is the probability that you will be able to take the tlight? What is thls probabllity If you are the third person on the standby lst?

Explanation / Answer

a)P(flight accomodate all pessanger)=P(X<=50)=1-0.06-0.05-0.03-0.02-0.01=0.83

b)

P(not all can be accomodated)=1-0.83 =0.17

c)

P(able to take the flight)=P(at most 49 pessanger appears)=0.04+0.10+0.12+0.14+0.26=0.66

d)

P(able to take the flight)=P(at most 47 passenger appears)=0.04+0.1+0.12=0.26

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