II: A dashboard warning light is supposed to flash (F) if a car’s oil pressure i
ID: 3378457 • Letter: I
Question
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).
Explanation / Answer
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]
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3.
P(L|F) = P(L) P(F|L) / P(F)
= 0.10*0.95/0.113
= 0.840707965 [ANSWER]