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## Homework Statement

The problem statement is given below:

## Homework Equations

## The Attempt at a Solution

Here is my attempt so far:

I'm sure questions 1 - 4 have been answered. Question 5 is what concerns me.

I need to find ##P(C' | D')##, which is the probability a good item is identified, given a good item is chosen.

The probability a good item is chosen is ##P(D') = 0.991##.

Now I need the probability the good item chosen is identified as a good item. From question 4), the chance a good item is identified is ##P(C') = 0.9861##.

Would that mean of the ##99.1##% of good items, ##98.61##% of them will be identified as good items? So we would get:

$$P(C' | D') = 0.991 * 0.9861 = 0.977$$

I am not confident about this. Any help would be appreciated.

Thank you.