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

Step2: Substitute the given values

We know that $P(B) = 0.04$, $P(B\cap C)=0.01$, and $P(B\cup C)=0.06$. Substituting these values into the formula $0.06 = 0.04+P(C)-0.01$.

Step3: 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 $P(C)$: $P(C)=0.06 - 0.03=0.03$.

Answer:

3 percent