MAT 202 Conditional Probability and Independence Checkpoint 2

Conditional Probability and Independence


Conditional Probability and Independence
Checkpoint 2
Step 1 of 1

Question 1 of 5 Points: 10 out of 10
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.
79%
(iii)
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
Good job! We need to find P(Pr and G). Using the General Multiplication Rule, P(Pr and G) =
P(Pr) * P(G | Pr) = .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



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, • L—the skill was Learned successfully

Question 2 of 5 Points: 10 out of 10
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

Good job! There is a 95% chance of learning the skill if method A is used. This translates to: P(L
| A) = .95. There is an 80% chance of learning the skill if method B is used. This translates to:
P(L | B) = .80. Method A is used 25% of the time. This translates to P(A) = .25. Since P(A) = .25,
P(not A) = P(B) = .75.

Question 3 of 5 Points: 10 out of 10
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?




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