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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

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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

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103 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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