Question

When someone buys a ticket for an airline​ flight, there is a 0.0981 probability that the person will not show up for the flight. A certain jet can seat 13 passengers. Is it wise to book 15 passengers for a flight on the​ jet? Explain.

Determine whether or not booking 15 passengers for 13 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. ​(Round to four decimal places as​ needed.)

A.It is 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 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 not a wise decision because the probability that there are not enough seats on the jet is ___ ​So, overbooking is an unlikely event.

D.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.

Answer 1

Let X be the number of passengers will show up for the flight

p=1-0.0981 = 0.9019

n=15

and probability is given by

P(X=x) = C(n,x)*px*(1-p)(n-x)

P ( X =    14   ) = C(15,14) * 0.9019^14 * (1-0.9019)^1 =            0.3467
P ( X =    15   ) = C(15,15) * 0.9019^15 * (1-0.9019)^0 =            0.2125

P(overbooking) = P(X=14) + P(X=15) =0.3467 + 0.2125 = 0.5592

So,

D.It is not a wise decision because the probability that there are not enough seats on the jet is 0.5592.

So, overbooking is not an unlikely event.