Question

At a production process, the produced items are tested for defects. A defective unit is classified as such with probability 0.9, whereas a correct unit is classified as such with probability 0.85. Furthermore, 10% of the produced units are defective. Compute the conditional probability that a unit is defective, given that is has been classified as such.

Answer 1

Answer:

We use Baye's theorem:  P(A)P(B|A) = P(B)P(A|B)

with (A) being defective and

(B) marked as defective

we have to find P(B) = P(A).P(B|A) + P(¬A)P(B|¬A). .......eq(2)

Since  P(A) = 0.1 and P(B|A)=0.9,

P(¬A) = 1 - P(A) = 1 - 0.1 = 0.9

and

P(B|A¬) = 1 - P(¬B|¬A) = 1 - 0.85 = 0.15

put these values in eq(2)

P(B) = (0.1 × 0.9) + (0.9 × 0.15)

       = 0.225 put this in eq(1) and solve for P(B)

P(B) = 0.4