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

Which of the following is the correct representation of the information that is provided to us?

   P(A) = .75, P(B) = .25, P(L | A) = .80, P(L | B) = .95

   P(A) = .75, P(B) = .25, P(A | L) = .80, P(B | L) = .95

   P(A) = .75, P(B) = .25, P(A and L) = .80, P(B and L) = .95

   P(A | L) = .75, P(B | L) = .25, P(L | A) = .80, P(L | B) = .95

   P(A and L) = .75, P(B and L) = .25, P(L | A) = .80, P(L | B) = .95

What is the probability that a randomly chosen worker will learn the skill successfully?

   P(L) = .75 * .80 = .60

   P(L) = .25 * .95 = .2375

   P(L) = .75 * .25 + .80 * .95 = .9475

   P(L) = .75 * .95 + .25 * .80 = .9125

   P(L) = .75 * .80 + .25 * .95 = .8375

A worker learned the skill successfully. What is the probability that he was taught by method A?

(a) .75×.80=.60.75×.80=.60

(b) .80

(c) .25×.95.75×.80 + .25×.95≈.2836.25×.95.75×.80 + .25×.95≈.2836

(d).75×.80.75×.80 + .25×.95≈.7164.75×.80.75×.80 + .25×.95≈.7164

(e) .75×.80.80 + .95≈.3429

Answer 1