2.4.42. A dashboard warning light is supposed to flash red if a car’s oil pressure is too low. On a certain model, the probability of the light flashing when it should is 0.99; 2% of the time, though, it flashes for no apparent reason. If there is a 10% chance that the oil pressure really is low, what is the probability that a driver needs to be concerned if the warning light goes on?

The probability that a driver needs to be concerned if the warning light goes on is 0.8462.

Step-by-step explanation:

The conditional probability of an X given that another event Y has already occurred is:

The law of total probability states that:

Denote the events as follows:

A = the light flashes

B = the oil pressure is low.

Given:

Compute the probability that the light flashes using the law of total probability as follows:

Compute the probability that the oil pressure is low given that the light flashes as follows:

Thus, the probability that a driver needs to be concerned if the warning light goes on is 0.8462.