After a production run,it was found that 10% of the units produced had a faulty weld and 5% had both a defective paint job and a faulty weld.If a unit is randomly selected from this run and it has a faulty weld,what is the probability that it also has a defective paint job?

Question

Quizplus · Accepted Answer

We need to find the probability of a unit having a defective paint job given that it has a faulty weld. This can be calculated using the conditional probability formula as follows:

P(defective paint job | faulty weld) = P(defective paint job and faulty weld) / P(faulty weld)

We know that 5% of the units have both a defective paint job and a faulty weld. Also, 10% of the units have a faulty weld. Therefore,

P(defective paint job and faulty weld) = 5% of total units
P(faulty weld) = 10% of total units

Substituting these values in the formula above, we get:

P(defective paint job | faulty weld) = (5% / 10%) = 50%

Therefore, the probability of a unit having a defective paint job given that it has a faulty weld is 50%. The best choice is B.

After a Production Run,it Was Found That 10% of the Units