Question

7. A certain sports car model has a 0.07 probability of defective steering and a 0.11 probability of defective brakes. Erich S -E just purchased one of the models. If the two problems are statistically independent, determine the probability

a. Erich’s car has both defective steering and defective brakes.

b. Erich’s car has neither defective steering nor defective brakes.

c. Erich’s car has either defective steering only or defective brakes only (meaning exactly one of the two, but not both, defects).

Answer 1

Given data :

Let A be the car has defective steering

Let B be the car has defective brakes

P(A) = 0.07

P(B) = 0.11

a)P(Erich’s car has both defective steering and defective brakes) = P(A B)

P(A B) = P(A) *P(B) = 0.07*0.11 = 0.0077

Probability that erich’s car has both defective steering and defective brakes is 0.0077

b) P(Erich’s car has neither defective steering nor defective brakes.) = P(A " B")

P(A " B") = P(A') *P(B')

P(A') = 1- 0.07 = 0.93

P(B') = 1-0.11 = 0.89

P(A " B") = 0.93*0.89 = 0.8277

Probability that Erich’s car has neither defective steering nor defective brakes is 0.8277

c) P(Erich’s car has either defective steering only or defective brakes only )

P(A U B) = P(A) +P(B) - P(A B)

P(A U B) = 0.07+0.11 - 0.0077 = 0.1723

P(A U B) = 0.1723

probability that Erich’s car has either defective steering only or defective brakes only