Three airport terminals are to be selected for architectural

Three airport terminals are to be selected for architectural and engineering design improvement. The desirable airport terminals should be such that in the last 10 years the proportion of their passengers is less than s. Suppose there is a large number of airport terminals available for selection. Moreover, suppose that for each airport terminal available for selection, the proportion of its passengers follows a beta distribution with parameters = = 3.

(a) What is the probability that at most k airport terminals whose proportion of passengers is greater or equal to s are selected before the third airport terminal with proportion of passengers less than s is selected.

(b) Compute the above probability for s = 1 3 and k = 2

*My class uses Probability and Statistics for Engineers and Scientists 9th edition

Solution