Two methods A and B are available for teaching a certain ind

Two methods, A and B are available for teaching a certain industrial skill. The failure rate is 20% for A and 10% for B. However B is more expensive and used only 30% of the time (A is used the other 70%). A worker is taught the skill by one of the methods but fails to learn it correctly. What is the probability that she was taught by method A?

Solution

Let

A, B = the method used
F = fails to learn

Thus,

P(A|F) = P(A) P(F|A) / P(F)

As

P(F) = P(A) P(F|A) + P(B) P(F|B) = 0.70*0.20 + 0.30*0.10 = 0.17

Then

P(A|F) = 0.70*0.20 / 0.17 = 0.823529412 [answer]