Question

An airport limousine can accommodate up to four passengers on any one trip. The company will accept a maximum of six reservations for a trip, and a passenger must have a reservation. From previous records, 40% of all those making reservations do not appear for the trip. Answer the following questions, assuming independence wherever appropriate. (Round your answers to three decimal places.)

(a) If six reservations are made, what is the probability that at least one individual with a reservation cannot be accommodated on the trip?
(b) If six reservations are made, what is the expected number of available places when the limousine departs?

Answer 1

0.23328,2.4

Explanation:

Given that an airport limousine can accommodate up to four passengers on any one trip. The company will accept a maximum of six reservations for a trip, and a passenger must have a reservation.

Assuming independence we can say persons who do not show up is binomial with p = 0.4 and n = 6

a) If six reservations are made, what is the probability that at least one individual with a reservation cannot be accommodated on the trip

=
`P(X\leq 1)\\=0.23328`

b) Expected no of available places = E(x)=
`np = 6(0.4) = 2.4`