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, 26 of them own at least one hybrid car, 12 of them own at least one electric car, and 2 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

Solution:

You have a (universal) set U of 80 members and the subsets
- H of 26 members (own at least one hybrid car)
- E of 12 members (own at least one electric car) and
- HE of 2 members (own at least one hybrid and at least one electric car).
Notice that the subset HE is the intersection of subsets H and E.

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

The number of those who own only hybrid car is H - HE = 26 - 2 = 22.
The probability under the question is 22/80 = 11/40 = 0.275 = 27.5%.

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

The number of those who own at least one of hybrid or at least one electric car is
H + E - HE = 26 + 12 - 2 = 36.   
The rest of the 80 members of the club, i.e. 80 - 36 = 44 members, do not own any AFV car.

So the probability under this question is 44/80 = 11/20 = 0.55 = 55%.