Question

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

Answer 1

Let the probability of a brake defect be P(B), the probability of a chain defect be P(C) then the probability of a brake and a chain defect is P(B ∩ C) and the probability of a brake or a chain defect P(B ∪ C).

Given that P(B) = 4%, P(C) = ?, P(B ∩ C) = 1%, P(B ∪ C) = 6%.

P(B ∪ C) = P(B) + P(C) - P(B ∩ C)
Thus, P(C) = P(B ∪ C) + P(B ∩ C) - P(B) = 6% + 1% - 4% = 3%

Answer 2

If the probability of a defect with the brakes or the chain is 6 percent, the probability of a chain defect is 3%.

Probability

Using this formula

P(C) = P(B ∪ C) + P(B ∩ C) - P(B)

Where:

Brake defect=  P(B) = 4%

Chain defect= P(C) = ?

Brake defect and chain defect =P(B ∩ C) = 1%

Brake defect or chain defect=P(B ∪ C) = 6%

Let plug in the formula

P(C) = 6% + 1% - 4%

P(C)= 3%

Therefore the probability of a chain defect is 3%.

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