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 only, and that 6% of the trucks have defective brake linings only. If 87% of the trucks have neither defect, what percentage of the trucks have both defects?

Answer 1

Answer: Probability of trucks having both defects is 4%.

Explanation:

Since we have given that

Probability of trucks having defective brake linings only = 6%

Probability of trucks having defective steering only = 3%

Probability of trucks having neither defect = 87%

Probability of trucks having either defect - 100 - 87 = 13%

Let the probability of trucks having both defects be 'x'.

P(defective brake lining) = P(B) = 0.06+x

P(defective steering) = P(S) = 0.03+x

So, Probability of the trucks having both defects is given by

`P(S\cup B)=P(S)+P(B)-P(S\cap B)\\\\0.13=0.03+x+0.06+x-x\\\\0.13-0.03-0.06=2x-x\\\\0.04=x`

So, Probability of trucks having both defects is 4%.