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? 1.5 percent 2 percent 2.5 percent 3 percent

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

Answer

Explanation:

Step1: Recall the formula for the probability of the union

We use the formula $P(A\cup B)=P(A)+P(B)-P(A\cap B)$, where $A$ is the event of a brake - defect and $B$ is the event of a chain - defect. Let $P(A)$ be the probability of a brake defect, $P(B)$ be the probability of a chain defect, and $P(A\cup B)$ be the probability of a brake or chain defect, and $P(A\cap B)$ be the probability of both a brake and chain defect.

Step2: Substitute the given values into the formula

We know that $P(A) = 4%=0.04$, $P(A\cup B)=6% = 0.06$, and $P(A\cap B)=1%=0.01$. Substituting 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: $0.04 + P(B)-0.01=0.03 + P(B)$. Then, solve for $P(B)$: [ \begin{align*} 0.06&=0.03 + P(B)\ P(B)&=0.06 - 0.03\ P(B)&=0.03 \end{align*} ] Since $P(B)$ is the probability of a chain defect, and $0.03$ as a percentage is $3%$.

Answer:

3 percent