I. Suppose that among the pre-owned cars available in a large dealership, 80% ha

Question

I. Suppose that among the pre-owned cars available in a large dealership, 80% have air conditioning, 70% have a CD player, and 65% have both. a) Determine the proportion of these cars that have neither air conditioning nor a CD player. As always, show your method of solution. b) Determine the conditional probability that a randomly selected car has a CD player, given that it has air conditioning c) Are the events (randomly selected car has air conditioning) and (randomly selected car has a CD player) independent? Justify your answer. spegiamdemly selected can has a CD player) disjoint? Explain briefly

Explanation / Answer

P(air conditioning) = 0.8

P(CD player) = 0.7

P(both) = 0.65

a) P(neither air conditioning nor a CD player) = 1 - P(at least one of air conditioning or CD player)

                                                    = 1 - (P(air conditioning) + P(CD player) - P(both))

                                                    = 1 - (0.8 + 0.7 - 0.65)

                                                    = 0.15

b) P(CD player | air conditioning) = P(both) / P(air conditioning) = 0.65 / 0.8 = 0.8125

c) Since, P(CD player | air conditioning) is not equal to P(CD player) , the two events are not independent.

d) Since, P(both) is not equal to zero , the two events are not disjoint.

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---