Question

A survey was conducted by the local chapter of an environmental club regarding the ownership of alternative fuel vehicles (AFVs) among the members of the group. An AFV is a vehicle that runs on fuel other than petroleum fuels (petrol and diesel). It was found that of the 80 members of the club surveyed, 30 of them own at least one hybrid car, 18 of them own at least one electric car, and 8 of them own at least one hybrid and at least one electric car. (Enter your answers to three decimal places.)

(a) If a member of the club is surveyed, what is the probability that he or she owns only hybrid cars?

(b) If a member of the club is surveyed, what is the probability that he or she owns no alternative fuel vehicles?

Answer 1

a) P(only hybrid cars) = P(at least one hybrid car) - P(at least one hybrid and at least one electric car)

                                   = 30/80 - 8/80

                                   = 0.275

b) P(no AFVs) = 1 - P(at least one hybrid or at least one electric car)

                        = 1 - (P(at least one hybrid car) + P(at least one electric car) - P(at least one hybrid and at least one electric car))

                        = 1 - (30/80 + 18/30 - 8/30)

                        = 1 - 0.708

                        = 0.292