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If faults in cars are reported correctly 85% of the time, but it is known that 35% are reported as faults when it was really due to poor handling, even 30% if they are due to faults, calculate the probability that yes be it due to failure when it was reported that way

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Answer to a math question If faults in cars are reported correctly 85% of the time, but it is known that 35% are reported as faults when it was really due to poor handling, even 30% if they are due to faults, calculate the probability that yes be it due to failure when it was reported that way

Expert avatar
Birdie
4.5
104 Answers
1. Calculate the probability of no-fault reports:

P(A^c) = 1 - P(A) = 1 - 0.30 = 0.70

2. Calculate the total probability of a report:

P(B) = P(B \mid A) P(A) + P(B \mid A^c) P(A^c) = (0.85 \cdot 0.30) + (0.35 \cdot 0.70) = 0.50

3. Use Bayes' theorem to calculate the probability of an actual fault given a report:

P(A \mid B) = \frac{P(B \mid A) P(A)}{P(B)} = \frac{0.85 \cdot 0.30}{0.50} = 0.51

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