# Marginal & Conditional Probabilities

A Survey of top executives revealed that 35 percent of them regularly read Time magazine,

20 percent read Newsweek, and 40 percent read U.S. News and World Report. Ten percent

read both Time and U.S. News and World Report. What is the probability that a particular

top executive reads either Time or U.S. News and World Report regularly?

2. A local bank reports that 80 percent of its customers maintain a checking account, 60

percent have a savings account, and 50 percent have both.

a) If a customer is chosen at random,what is the probability the customer has either a ^

checking or a savings account?

b) What is the probability the customer does not have either a checking or a savings

account?

3. You have a bag that contains the following colors of marbles: 4 blue, 3 red, 2 green, and 1

yellow. What is the probability of drawing each of the following from the bag?

a. 1 blue,1 red, and 1 yellow (without replacement)

b. 1 red and 2 green (without replacement)

c. A green or a yellow marble in a single draw

4. Refer to the contingency table shown below, (a) Calculate each probability (i-iv).

a.P(S)

b.P(W)

c.P(S/B)

d.P(S and W)

Males Aged 18-24

White smoker =290

Black smokers=30

Total smokers=320

White nonsmoker=560

Black nonsmoker=120

Total nonsmokers=680

#### Solution Preview

Please see the attachment.

Probability

A Survey of top executives revealed that 35 percent of them regularly read Time magazine, 20 percent read Newsweek, and 40 percent read U.S. News and World Report. Ten percent read both Time and U.S. News and World Report. What is the probability that a particular top executive reads either Time or U.S. News and World Report regularly?

Answer

Let A and B be the events that the top executive read Time magazine and U.S. News and World Report respectively.

Given that, P (A) = 0.35, P (B) = 0.4 and P (A ∩ B) = 0.1

P (The top executive reads either Time or U.S. News and World Report)

= P (A U B)

= P (A) + P (B) - P (A ∩ B)

= 0.35 + 0.4 - 0.1

= 0.65

2. A local bank reports that 80 percent of its customers maintain a checking account, 60 percent have a ...

#### Solution Summary

The solution provides step by step method for the calculation of probabilities and conditional probabilities. Formula for the calculation and Interpretations of the results are also included.