
Baye's Rule 2
Two methods, A and B, are available for teaching a skill. The failure rate for method A is 30% and 10% for B. Method is more expensive, however, and hence used only 20% of the time (A 80%). A worker is taught the skill by one of two methods but fails to learn the skill. What is the probability he was taught by method A?
I am looking for P(A failed)?
Also, I am not sure hoe set this up if that is correct.

$\displaystyle P(AF)=\dfrac{P(FA)P(A)}{P(FA)P(A)+P(FB)P(B)}$
Is that what you are looking for?