An airport limousine can accommodate up to tour passengers on any one trip. The

Question

An airport limousine can accommodate up to tour 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. If six reservations are made, what is the probability that at least one individual with a reservation cannot be accommodated on the trip? 0.23328 If six reservations are made, what is the expected number of available places when the limousine departs? 0.76672 Suppose the probability distribution of the number of reservations made is given in the accompanying table. Let X denote the number of passengers on a randomly selected trip. Obtain the probability mass function of X.

Explanation / Answer

Let X be the random variable that number of people with reservations that show up for the trip,

Here X ~ Binomial(n = 6, p = 60% = 0.6)

The pmf of X=x is,

P(X=x) = (6 C x) * 0.6x * (1 - 0.6)(6-x)   x = 0,1,2,..........n

In the first part e have to find P(X >=1).

P(X>=1) = 1 - P(X=0)

P(X=0) = (6 C 0) * 0.60 * (1 - 0.6)(6-0) = 0.0041

P(X>=1) = 1 - 0.0041 = 0.9959

Expected value = n*p = 6*0.6 = 3.6

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