A cruise liner knows that passengers who purchase tickets on their cruises have

Question

A cruise liner knows that passengers who purchase tickets on their cruises have a 96% chance of making it on the cruise. Suppose on the day of departure, a particular ship has booked 20 first-class cabins. What is the probability that all of the 20 occupants who booked first-class cabins show up? What is the probabilty that at least one of the occupants who booked first-class cabins fails to show up? Suppose the cruise liner chooses to overbook, and allows 21 occupants to book first-class cabins, even though they only have 20 available. What is the probability that one of the occupants shows up and no first-class cabin is avaliable because of overbooking?

Explanation / Answer

P(passeger showing up ) = 0.96

What is the probability that all of the 20 occupants who booked first-class cabins show up?

P = 0.96^20 = 0.442

What is the probabilty that at least one of the occupants who booked first-class cabins fails to show up?

P = 1- all show up = 1-0.442 = 0.558

Suppose the cruise liner chooses to overbook, and allows 21 occupants to book first-class cabins, even though they only have 20 available. What is the probability that one of the occupants shows up and no first-class cabin is avaliable because of overbooking?

all 21 show up

P = 0.96^21 = 0.424

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