Question

In a certain year, the probability that a randomly selected vehicle would be involved in a deadly tire-related accident was approximately 4 × 10−6 whereas the probability that a tire-related accident would prove deadly was 0.05. What was the probability that a vehicle would be involved in a tire-related accident?

Answer 1

The probability that a vehicle would be involved in a tire-related accident is
`P(TRA)=8x10^(-5)`

Explanation:

We need to calculate the probability that a vehicule would be involved in a tire-related accident.

We know that, given a tire-related accident (TRA), the probability of it being deadly (D) is 0.05. That is:

`P(D|TRA)=0.05`

We also know that the probability of being involved in a deadly tire-related accident is 0.000004 . We can express that as the probability of having a TRA multiplied by the probability of it being deadly:

`P(D|TRA)*P(TRA)=0.000004`

Merging the two expressions we have:

`P(TRA)=0.000004/P(D|TRA)=0.000004/0.05=0.00008=8x10^(-5)`