THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A manufacturer of automobiles conducted a market survey.Eighty percent of the customers want better fuel efficiency,while 55% want a vehicle navigation system and 45% percent want both features.
-The probability that a person wants a vehicle navigation system given that he wants a better fuel efficiency is approximately:
A)0.80
B)0.40
C)0.45
D)0.56

Question

Quizplus · Accepted Answer

The probability that a person wants a vehicle navigation system given that they want better fuel efficiency is found using the formula for conditional probability: P(A|B) = P(A and B) / P(B). Here, A is the event of wanting a vehicle navigation system, and B is the event of wanting better fuel efficiency. Given that 45% want both features and 80% want better fuel efficiency, P(A|B) = 0.45 / 0.80 = 0.5625, which is approximately 0.56.