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? 1.5 percent 2 percent 2.5 percent 3 percent

Explanation:

Step1: Recall the formula for \(P(A\cup B)\)

The formula for the probability of the union of two events \(A\) and \(B\) is \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\). Let \(A\) be the event of a brake defect and \(B\) be the event of a chain defect. We know \(P(A) = 0.04\), \(P(A\cap B)=0.01\), and \(P(A\cup B)=0.06\).

Step2: Substitute the known values into the formula

Substitute into \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\), we get \(0.06 = 0.04+P(B)-0.01\).

Step3: Solve for \(P(B)\)

First, simplify the right - hand side of the equation: \(0.04 - 0.01+P(B)=0.03 + P(B)\). Then, solve the equation \(0.06=0.03 + P(B)\) for \(P(B)\). Subtract \(0.03\) from both sides: \(P(B)=0.06 - 0.03\).

Answer:

\(3\) percent.