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)*p^{x}*(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.**

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