[TEX]

Firstly, I am giving calculations for the second answer

Let us define the events:

The set up was correct.

The set up was wrong.

**E=**The item is acceptable.

**D=**The item is not acceptable (defective)

We know

Probability that the set up was correct =0.8

Probability that the set up was wrong =0.2

Probability the item is acceptable given the information that the set up is correct =0.9

=0.4

We are required to find the probability that the set up is correct given that the 3 items are acceptable, i-e

=0.99310345

From the above calculations, i think you will know the calculations i have made for the first answer.