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