When someone buys a ticket for an airline flight, there is a 0.0985 probability

Question

When someone buys a ticket for an airline flight, there is a 0.0985 probability that the person will not show up for the flight. A certain jet can seat 8 passengers. Is it wise to book 10 passengers for a flight on the jet? Explain. Determine whether or not booking 10 passengers for 8 seats on the jet is a wise decision. Select the correct choice below and fill in the answer box in that choice with the probability that there are not enough seats on the jet. A. It is not a wise decision because the probability that there are not enough seats on the jet is So, overbooking is an unlikely event. B. It is not a wise decision because the probability that there are not enough seats on the jet is So, overbooking is not an unlikely event. C. It is a wise decision because the probability that there are not enough seats on the jet is So, overbooking is not an unlikely event. D. It is a wise decision because the probability that there are not enough seats on the jet is So, overbooking is an unlikely event.

Explanation / Answer

Let, X be the number of passenger showing up.

Here X ~ binomial (n = 10, p = 0.0985)

The pmf of X=x is,

P(X=x) = (10 C x) * 0.0985x * (1 - 0.0985)(10-x)   x = 0,1,...........,n

Here we have to find P(X >8).

P(X> 8) = P(X=9) + P(X=10)

= (10 C 9) * 0.09859 * (1 - 0.0985)(10-9) + (10 C 10) * 0.098510 * (1 - 0.0985)(10-10)   

= 7.8685E-09 + 8.5973E-09 = 7.95447E-09 = 0.0000

The corresponding probability being too low, booking 10 passengers is a wise decision.

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