Question

Two methods, A and B, are available for teaching a certain industrial skill. The failure rate is 30% for method A and 10% for method B. Method B is more expensive, however, and hence is used only 20% of the time. (Method A is used the other 80% of the time.) A worker is taught the skill by one of the two methods, but he fails to learn it correctly. What is the probability that he was taught by using method A

Answer 1

Probability that he was taught by using method A is 14/17

Explanation:

Following probabilities are given -

P (F|A) = 0.2

P (F|B) = 0.1

P (A) = 0.7

P (B) = 0.3

Now, P(A|F) = P (F/ P (F + P (F}

P(A|F) = (0.2*0.7)/( (0.2*0.7)+(0.1*0.3)) = 14/17