Hey guys, just 3 questions this time...

1. Three different machines M1, M2, and M3 were used for producing a large

batch of similar manufactured items. Suppose that 20% of the items were

produced by M1, 30% by M2, and 50% by M3. Suppose further that 1% of the items produced by M1 are defective, that 2% of the items produced by M2 are defective, and that 3% of the items produced by M3 are defective.

i) Suppose one item is selected at random from the entire batch and it

is found to be defective. Determine the probability that this item

was produced by M2.

ii) Suppose one item is selected at random from the entire batch and it

is found to be nondefective. Determine the probability that it was

produced by M2.

**My answers:**
We must use conditional probability.

i)

Code:

M1 M2 M3
Items Produced (Ip) : 0,2 0,3 0,5
Items Defective (Id) : 0,01 0,02 0,03
Items not-Defect. (In): 0,99 0,98 0,97

%

ii) P(M2 \cap In) = P(M2) \cdot P(In | M2)

%

[snip]