Question

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? When the warning light goes on, what is the probability that the oil pressure is low?

Answer 1

0.8462 or 84.62%

Explanation:

The probability that the light flashes is given by the probability of it flashing when it should added to the probability of flashing when it should not:

`P(F) = P(O)*P(F_O)+P(N)*P(F_N)\\P(F) =0.10*0.99 + (1-0.10)*0.02\\P(F) = 0.117`

The probability that the oil pressure is low (driver needs to be concerned) is given by the probability that oil is low and the light flashes divided by the probability that the light flashes.

`P(O|F) =(P(O_F)*P(O))/(P(F)) \\P(O|F) =(0.99*0.10)/(0.117)\\ P(O|F) =0.8462`

When the warning light goes on, there is a 0.8462 probability that the oil pressure is low.