Question

These days with the cost of a college education it is important to be able to graduate with a bachelors degree in 4 years. The National Association of Independent Colleges and Universities (NAICU) certainly would encourage students to attend independent schools. They provided the following information:

(i)	20% of all college students attend private colleges and universities.
(ii)	55% of all college students graduate in 4 years.
(iii)	79% of students attending private colleges and universities graduate in 4 years.

What is the probability that a randomly chosen student attended a private school and graduated in 4 years?

   .55 / .79 = .6962

   .20 / .55 = .3636

   .20 / .79 = .2532

   .55 * .79 = .4345

   .20 * .55 = .11

   .20 * .79 = .158

The next four questions refer to the following information:

Two methods, A and B, are available for teaching a certain industrial skill. There is a 95% chance of successfully learning the skill if method A is used, and an 80% chance of success if method B is used. However, method A is substantially more expensive and is therefore used only 25% of the time (method B 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
• Question 2 of 5
• Which of the following is the correct representation of the information that is provided to us?
•    P(A) = .25, P(B) = .75, P(A | L) = .95, P(B | L) = .80
•    P(A) = .25, P(B) = .75, P(L | A) = .95, P(L | B) = .80
•    P(A) = .25, P(B) = .75, P(A and L) = .95, P(B and L) = .80
•    P(A and L) = .25, P(B and L) = .75, P(L | A) = .95, P(L | B) = .80
•    P(A | L) = .25, P(B | L) = .75, P(L | A) = .95, P(L | B) = .80
• Question 3 of 5
• Again we have two methods, A and B, available for teaching a certain industrial skill. There is a 95% chance of successfully learning the skill if method A is used, and an 80% chance of success if method B is used. However, method A is substantially more expensive and is therefore used only 25% of the time (method B is used the other 75% of the time).
• Which of the following is the correct probability tree for this problem?

Again we have two methods, A and B, available for teaching a certain industrial skill. There is a 95% chance of successfully learning the skill if method A is used, and an 80% chance of success if method B is used. However, method A is substantially more expensive and is therefore used only 25% of the time (method B is used the other 75% of the time).

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) = .25 * .95 + .75 * .80 = .8375

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

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

gain we have two methods, A and B, available for teaching a certain industrial skill. There is a 95% chance of successfully learning the skill if method A is used, and an 80% chance of success if method B is used. However, method A is substantially more expensive and is therefore used only 25% of the time (method B is used the other 75% of the time).

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

.25×.95=.2375.25×.95=.2375

.95.95

   .25×.95.95 + .80≈.1357.25×.95.95 + .80≈.1357

   .75×.80.25×.95 + .75×.80≈.7164.75×.80.25×.95 + .75×.80≈.7164

   .25×.95.25×.95 + .75×.80≈.2836.25×.95.25×.95 + .75×.80≈.2836

Answer 1