Question

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A bicycle manufacturer is studying the reliability of one of its models. The study finds that the probability of a brake defect is 4 percent and the probability of both a brake defect and a chain defect is 1 percent.

If the probability of a defect with the brakes or the chain is 6 percent, what is the probability of a chain defect?

1.5 percent
2 percent
2.5 percent
3 percent

Answer 1

Let B = brake defect, C = chain defect. Use inclusion-exclusion:

P(B ∪ C) = P(B) + P(C) − P(B ∩ C).

0.06 = 0.04 + P(C) − 0.01 → P(C) = 0.06 − 0.04 + 0.01 = 0.03 = 3%.

Answer: 3 percent.