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

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 $P(A\cap B)$ be the probability of both a brake and a chain defect, and $P(A\cup B)$ be the probability of a brake or a chain defect.
We know that $P(A) = 0.04$, $P(A\cap B)=0.01$, and $P(A\cup B)=0.06$.

Step2: Rearrange the formula to solve for $P(B)$

From $P(A\cup B)=P(A)+P(B)-P(A\cap B)$, we can solve for $P(B)$ by rearranging the formula: $P(B)=P(A\cup B)+P(A\cap B)-P(A)$.

Step3: Substitute the known values

Substitute $P(A) = 0.04$, $P(A\cap B)=0.01$, and $P(A\cup B)=0.06$ into the formula for $P(B)$.
$P(B)=0.06 + 0.01-0.04$.
$P(B)=0.03$.

Answer:

3 percent