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 the probability of the union

Let \(P(B)\) be the probability of a brake - defect, \(P(C)\) be the probability of a chain - defect, and \(P(B\cap C)\) be the probability of both a brake and a chain defect. The formula for \(P(B\cup C)\) is \(P(B\cup C)=P(B)+P(C)-P(B\cap C)\).

Step2: Identify the given values

We are given that \(P(B) = 0.04\), \(P(B\cap C)=0.01\), and \(P(B\cup C)=0.06\).

Step3: Substitute the values into the formula

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

Step4: Solve for \(P(C)\)

First, simplify the right - hand side of the equation: \(0.04 + P(C)-0.01=0.03 + P(C)\). Then, solve for \(P(C)\): \(P(C)=0.06 - 0.03\). So, \(P(C)=0.03\).

Answer:

3 percent