Question

A production process produces an item. On average, 13% of all items produced are defective. Each item is inspected before being

shipped, and the inspector misclassifies an item 11% of the time. Please round the final answers to 3 decimal places.
Part 1 of 2
What proportion of the items will be "classified as good"?
P(classified as good)- 0.774
Correct Answer:
Learning Objective: The Multiplication Rules and Conditional Probability
0.788
X
8
99
do

Answer 1

We can start by finding the proportion of items that are not defective. Since 13% of items are defective, then 87% of items are not defective:

P(not defective) = 1 - P(defective) = 1 - 0.13 = 0.87

Next, we need to consider the probability that an item is classified as good by the inspector, given that it is actually good. This is the conditional probability:

P(classified as good | good) = 1 - P(misclassified | good)

We know that the inspector misclassifies an item 11% of the time, so the probability of correctly classifying a good item is:

1 - P(misclassified | good) = 1 - 0.11 = 0.89

Now we can use the multiplication rule to find the overall probability of an item being classified as good:

P(classified as good) = P(classified as good | good) * P(good)

P(classified as good) = 0.89 * 0.87 = 0.7743

Rounding to 3 decimal places, we get:

P(classified as good) ≈ 0.788

Therefore, approximately 0.788 or 78.8% of items will be classified as good