Probability that a truck stopped at a roadblock will have faulty brakes or badly worn tires are 0.23 and 0.24 respectively. Also, the probability is 0.38 that a truck stopped at the roadblock will have faulty brakes and/or badly worn tires. Find the probability that a truck stopped at this roadblock will have faulty brakes as well as badly worn tires.

 

Let:

P(A) = Probability of faulty brakes = 0.23

P(B) = Probability of badly worn tires = 0.24

P(A ∪ B) = Probability of faulty brakes and/or badly worn tires = 0.38

We know that:

P(A ∪ B) = P(A) + P(B) − P(A ∩ B)

Substitute values:

0.38 = 0.23 + 0.24 − P(A ∩ B)

⇒ P(A ∩ B) = 0.47 − 0.38 = 0.09

∴ The probability that a truck stopped at the roadblock will have faulty brakes as well as badly worn tires is 0.09.