At a car workshop, the probability that a car booked in has an engine fault is 0.18. Independently, the probability that the same car has a battery fault is...
Question 1 Report
At a car workshop, the probability that a car booked in has an engine fault is 0.18. Independently, the probability that the same car has a battery fault is 0.09.
- Work out the probability that a car booked in has both faults. (2)
- Work out the probability that a car booked in has neither fault. (2)
Answer Details
The two faults are independent, so the probability of both occurring, or of neither occurring, is found by multiplying the individual probabilities.
- (a) [2]. \(P(\text{both faults}) = 0.18 \times 0.09 = 0.0162\).
- (b) [2]. \(P(\text{no engine fault}) = 1-0.18=0.82\) and \(P(\text{no battery fault})=1-0.09=0.91\), so \(P(\text{neither fault}) = 0.82\times0.91 = 0.7462\).
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