a bicycle manufacturer is studying the reliability of one of its models. the study finds that the…

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?\no 1.5 percent\no 2 percent\no 2.5 percent\no 3 percent
Answer
Explanation:
Step1: Recall probability formula
Let $P(B)$ be the probability of brake - defect, $P(C)$ be the probability of chain - defect, and $P(B\cap C)$ be the probability of both brake and chain defect, $P(B\cup C)$ be the probability of brake or chain defect. The formula is $P(B\cup C)=P(B)+P(C)-P(B\cap C)$.
Step2: Substitute known values
We know that $P(B) = 0.04$, $P(B\cap C)=0.01$, and $P(B\cup C)=0.06$. Substituting 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, we have $0.06=0.03 + P(C)$. Subtract 0.03 from both sides: $P(C)=0.06 - 0.03=0.03$.
Answer:
3 percent