Question

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 working tires. What is the probability that a truck stopped at this roadblock will have faulty breaks as well as badly worn tires?

Answer 1

Let B be the event that a truck stopped at the roadblock will have faulty brakes and T be the event that it will have badly worn tires.

We have P(B) = 0.23

P(T) = 0.24

And P(B ∪ T) = 0.38

And P(B ∪ T) = P(B) + P(T) – P(B ∩ T)

So 0.38 = 0.23 + 0.24 – P(B ∩ T)

⇒ P(B ∩ T) = 0.23 + 0.24 – 0.38 = 0.09