Originally Posted by

**Vinod** [TEX]

Firstly, I am giving calculations for the second answer

Let us define the events:

$\displaystyle A_1=$The set up was correct.

$\displaystyle A_2=$The set up was wrong.

**E=**The item is acceptable.

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

We know $\displaystyle P(A_1)=$Probability that the set up was correct =0.8

$\displaystyle P(A_2)=$Probability that the set up was wrong =0.2

$\displaystyle P(E|A_1)=$Probability the item is acceptable given the information that the set up is correct =0.9

$\displaystyle P(E|A_2)=$=0.4

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

$\displaystyle P(A_1|E)=\frac{P(E|A_1)*P(A_1)^3}{P(E|A_1)*P(A_1)^ 3+P(E|A_2)*P(A_2)^3}$

$\displaystyle =\frac{0.9*(0.8)^3}{0.9*(0.8)^3+0.4*(0.2)^3}$=0.99310345

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