Event Probability

Too much enamel 0.25
Too little enamel 0.2
Uneven application 0.35
No defects noted 0.42

(1) What is the probability of a paint defect?

What is the probability of a paint defect which includes an improper amount of paint?

Because the probabilities add to greater than 1.0, some of them must be joint events (too much enamel and uneven, for instance)

Prob (paint defect)=1-Pr(nodefects)=.58

Pr(improper)=.45/.58

To find the probability of a paint defect, we need to add up the probabilities of all the events related to paint defects. In this case, the events related to paint defects are "Too much enamel," "Too little enamel," and "Uneven application."

The probability of a paint defect is calculated by adding the probabilities of these three events:

Probability of a paint defect = Probability of "Too much enamel" + Probability of "Too little enamel" + Probability of "Uneven application"

So, using the given probabilities:

Probability of a paint defect = 0.25 + 0.2 + 0.35 = 0.8

Therefore, the probability of a paint defect is 0.8, or 80%.

Now, to find the probability of a paint defect that includes an improper amount of paint, we need to consider only the events "Too much enamel" and "Too little enamel." These two events represent the improper amount of paint.

Probability of a paint defect with improper amount of paint = Probability of "Too much enamel" + Probability of "Too little enamel"

So, using the given probabilities:

Probability of a paint defect with improper amount of paint = 0.25 + 0.2 = 0.45

Therefore, the probability of a paint defect with an improper amount of paint is 0.45, or 45%.