II A dashboard warning light is supposed to flash F if a car

II: A dashboard warning light is supposed to flash (F) if a car’s oil pressure is low (L). In a certain car model:

– The probability of the light flashing when it should (i.e., when the pressure is really low) is 0.95;

– 2% of the time the light flashes for no apparent reason (i.e., when the oil pressure is not low);

– There is a 10% chance that the oil pressure is really low.

1. The problem gives you three pieces of information above. Express these three pieces

of information in terms of probabilities invovling event L and event F.

2. What is the probability that the warning light flashes?

3. Given that the warning light is flashing, what is the probability that a driver needs to be concerned (that the oil pressure is really low).

Solution

1.

The three events named, can be respectively expressed as

a. P(F|L) = 0.95
b. P(F|L\') = 0.02
c. P(L) = 0.10

2.

P(F) = P(L) P(F|L) + P(L\') P(F|L\')

= 0.10*0.95 + (1-0.10)*(0.02)

= 0.113 [ANSWER]

***************

3.

P(L|F) = P(L) P(F|L) / P(F)

= 0.10*0.95/0.113

= 0.840707965 [ANSWER]