Question

An airport limousine ca 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 20% of all those making reservations do not appear for the trip. Answer the following questions, assuming independence wherever appropriate

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?

c) Suppose the probability distribution of the number of reservation made is given in the accompanying table

Number of reservation 3 4 5 6

Probability .1 .2 .3 .4

Let X denote the number of passengers on a randomly selected trip. Obtain the probability mass function of X

Answer 1

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

If X = number of people with reservations that show up for the trip,

then X is B(4,.85)

P(an individual with reservations not accommodated)

b) If six reservations are made, what is the expected number of available places when the limousine departs?

If Y = number of available places on the limo when it leaves, so Y = 0,1,2,3,4,5,6 then,

And Z is B(6,0.80)