Question

A manufacturer of pickup trucks is required to recall all the trucks manufactured in a given year for the repair of possible defects in the steering column and defects in the brake linings. Dealers have been notified that 3% of the trucks have defective steering, and that 5% of the trucks have defective brake linings. If 94% of the trucks have neither defect, what percentage of the trucks have both defects

Answer 1

Answer: 2%

Step-by-step explanation:

Let A be the event of having defective steering and B be the vent of having defective brake linings.

Given: P(A)  = 0.03  P(B) = 0.05

P(neither A nor B ) = 0.94

Using formula: P(either A nor B) = 1- P(neither A nor B )

= 1-0.94

i.e.  P(either A nor B) =0.06

Using formula:P(A and B) = P(A)+P(B)-P(either A or B)

P(A and B) =0.03+0.05-0.06

= 0.02

Hence, the percentage of the trucks have both defects = 2%