Two methods, A and B, are available for teaching a certain industrial skill. The

Question

Two methods, A and B, are available for teaching a certain industrial skill. There is an 80% chance of successfully learning the skill if method A is used, and a 95% chance of success if method B is used. However, method B is substantially more expensive and is therefore used only 25% of the time (method A is used the other 75% of the time). The following notations are suggested: A—Method A is used. B—Method B is used. L—The skill was learned successfully. A worker learned the skill successfully. What is the probability that he was taught by method A? 0.75 * 0.80 = 0.60 0.80

Explanation / Answer

Ans:

P(A)=0.75

P(B)=0.25

P(L/A)=0.8

P(L/B)=0.95

Now,calculate:

P(A/L)=P(L/A)*P(A)/[P(L/A)*P(A)+P(L/B)*P(B)]

=0.8*0.75/[0.8*0.75+0.95*0.25]

=0.6/[0.6+0.2375]

=0.6/0.8375=0.7164

P(A/L)=0.7164

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