Question

The local automobile dealers released the results of a survey which revealed that 53% of all cars sold last month were purchase with an extended warranty, 27% were All Wheel Drive (AWD), and 15% had both and extended warranty and AWD. What is the probability one of these cars selected at random had neither an extended warranty nor AWD? (10 points) What is the probability that a car had an AWD vehicle unprotected by an extended warranty? (10 points) What is the probability a car with an extended warranty was an AWD vehicle? (10 points) Is having an AWD vehicle with an extended warranty a mutually exclusive event? Explain (10 points)

Answer 1

Let A denote the event that the car was purchased with an extended warranty

and Let B denote the event that the car purchased is AWD

P(A) = 0.53

P(B) = 0.27

P(A and B) = 0.15

Thus, P(A or B) = P(A) + P(B) - P(A and B)

= 0.65

Probability that one of these cars selected at random had neither an extended warranty nor AWD = 1 - P(A or B)

= 0.35

Probability that a car had an AWD vehicle unprotected by an extended warranty = P(B) - P(A and B) = 0.12

Probability that a car with an extended warranty was an AWD vehicle = P(B | A) = P(A and B)/P(A) = 0.283

No, having an AWD vehicle with an extended warranty is not a mutually exclusive event since the probability of both occuring together is not equal to 0