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 2.5 percent 2 percent 3 percent

Explanation:

Step1: Recall the formula for the probability of the union

$P(A\cup B)=P(A)+P(B)-P(A\cap B)$
Let $A$ be the event of a brake - defect and $B$ be the event of 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 $P(B)$

$P(B)=P(A\cup B)+P(A\cap B)-P(A)$

Step3: Substitute the known values

$P(B)=0.06 + 0.01-0.04$
$P(B)=0.03$

Answer:

3 percent