A certain university has 11 vehicles available for use by faculty and staff. Fiv

Question

A certain university has 11 vehicles available for use by faculty and staff. Five of these are vans and 9 are cars. On a particular day, only two requests for vehicles have been made. Suppose that the two vehicles to be assigned are chosen In a completely random fashlon from among the 14 (a) Let E denote the event that the first vehicle assigned is a van. What is P(E)? 3571 (b) Let / denote the probability that the second vehicle assigned is a van, what is pr | E)? (c) Use the results of Parts (a) and (b) to calculate P(E and (int: Use the definition of P(F | E).)

Explanation / Answer

a) P(E) = 5/14 = 0.3571

b) P(F | E) = P(second vehicle is van given that first vehicle is also a van) = 4/13 = 0.3077

c) P(F and E) = P(F | E) * P(E) = 4/13 * 5/14 = 0.1099

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