A certain university has 10 vehicles available for use by faculty and staff. Six

Question

A certain university has 10 vehicles available for use by faculty and staff. Six of these are vans and four 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 fashion from among the 10.

a) Let E denote the event that the first vehicle assigned is a van . What is P(E)?

b) Let F denote the event that the second vehicle assigned is a van. What is the P(F | E)?

c) Use the results from parts (a) and (b) to calculate the P(E and F).

Explanation / Answer

a) There are 6 vans out of 10 vehicles.

The probability that the first vehicle assigned is a van P(E) = 6/10 = 0.6.

b) P(F|E) is the probability that the second vehicle is a van.

There are 5 other vans out off 9 vehicles.

P(F|E) = 5/9 = 0.5556.

c) P(E and F) = P(F|E) P(E)

= 0.6 * 0.5556

= 0.33

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