refer to the following information:
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. A - method A is used
b. B - method B is used
c. L - the skill was learned successfullyWhich of the following is the correct representation of the information that is provided to us?

a. P(A)= .75, P(B) = .25, P(L |a) =. 80, P(L | B) = .95
b. P(A) = .75, P(B) = .25, P(A | L) = .80, P(B | L) = .95
c. P(A) = .75, P(B) = .25, P(A and L) = .80, P(B and L) = .95
d. P(A | L) = .75, P(B | L) = .25, P(L |a) = .80, P(L | B) = .95
e. P(A and L) = .75, P(B and L) = .25, P(L |a) = .80, P(L | B) = .95What is the probability that a worker will learn the skill successfully?

a. P(L) = .75 * .80 = .60
b. P(L) = .25 * .95 = .2375
c. P(L) = .75 * .25 + .80 * .95 = .9475
d. P(L) = .75 * .95 + .25 * .80 = .9125
e. P(L) = .75 * .80 + .25 * .95 = .8375

Step-by-step explanation:

Hello!

A: "Method A is used" and the probability of using it is P(A)= 0.75

B: "Method B is used" and its associated probability P(B)= 0.25

L: "The skill was learned"

"Learning the skill given that the method A is used" is a conditional probability, you can also say that "the skill was learned because method A was used", symbolically P(L/A)= 0.8

"Learning the skill given that method B is used" or "the skill was learned because method B was used", symbolically: P(L/B)= 0.95

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

Correct option: a.P(A)= .75, P(B) = .25, P(L |a) =. 80, P(L | B) = .95

2) What is the probability that a worker will learn the skill successfully?

You need to calculate the probability of L occuring, symbolically: P(L)

If you were to put all possible options in a contingency table:

A B Total

L P(A∩L) ; P(B∩L) ; P(A∩L) + P(B∩L) = P(L)

You can easily notice that the probability of learning the skill is the sum of the probabilities of "learning the skill and using method A" plus "learning the skill and using method B" These two intersections are unknown so first you apply the formula of conditional probability to find them out:

P(L/A)= P(A∩L)/P(A) ⇒ P(A∩L)= P(A)*P(L/A)= 0.75*0.80= 0.6

P(L/B)= P(B∩L)/P(B) ⇒ P(B∩L)= P(B)*P(L/B)= 0.25*0.95= 0.2375

P(L)= P(A∩L) + P(B∩L)= 0.6 + 0.2375= 0.8375

Correct option: e.P(L) = .75 * .80 + .25 * .95 = .8375

I hope you have a SUPER day!

d is correct

step-by-step explanation: