A certaln unlversity has 19 vehlcles avallable for use by faculty and staff. Fou

Question

A certaln unlversity has 19 vehlcles avallable for use by faculty and staff. Four of these are vans and 15 are cars. On a particular day, only two requests for vehlcles have been made. Suppose that the two vehicles to be assigned are chosen in a completely random fashion from among the 19. (a) Let E denote the event that the first vehicle assigned is a van. What is the value of P(E)? (b) Let F denote the probabllity that the second vehicle assigned is a van. What is the value of P(F IE)? (c) Use the results of parts (a) and (b) to calculate P(E n F)

Explanation / Answer

Solution : Given that total number of vehicles = 19 , number of vans = 4 , number of cars = 15

(a) Let E denote the event that the first vehicle assigned is a van

=> P(E) = 4/19 = 0.2105

(b) Let F denote the probability that the second vehicle assigned is a van

=> P(F/E) = 3/18 = 0.1667

(c) P(E ? F) = P(E)*P(F/E)
= (4/19)*(3/18)
= 0.0351

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