Question

The rental car agency has 30 cars on the lot. 10 are in great shape, 16 are in good shape, and 4 are in poor shape. Four cars are selected at random to be inspected. Do not simplify your answers. Leave in combinatorics form. What is the probability that: a. Every car selected is in poor shape b. At least two cars selected are in good shape. c. Exactly three cars selected are in great shape. d. Two cars selected are in great shape and two are in good shape. e. One car selected is in good shape but the other 3 selected are in poor shape.

Answer 1

a) P(all 4 are in poor shape) = 4C4 / 30C4

b) P(at least 2 cars are in good shape) = P(2 cars are in good shape) + P(3 cars are in good shape) + P(4 cars are in good shape)

                                                               = [16C2 * 14C2 / 30C4] + [16C3 * 14C1 / 30C4] + [16C4 * 14C0 / 30C4]

c) P(3 cars are in great shape) = 10C3 * 20C1 / 30C4

d) P(2 cars are in great shape and 2 cars are in good shape) = 10C2 * 16C2 / 30C4

e) P(One car is in good shape and 3 cars are in poor shape) = 16C1 * 4C3 / 30C4