# Probability Exclusive Events

1. The events A and B are mutually exclusive. Suppose P(A) = .30 and P(B) = .20. What is the probability of either A or B occurring? What is the probability that neither A nor B will happen?

2. A study by the National Park Service revealed that 50% of vacationers going to the Rocky Mountain region visit Yellowstone Park, 40 percent visit the Tetons, and 35 percent visit both.

a. What is the probability a vacationer will visit at least one of these attractions?

b. What is the probability .35 called?

c. Are the events mutually exclusive? Explain.

3. Customers experiencing technical difficulty with their Internet cable hookup may call an 800 number for technical support. It takes the technician between 30 seconds to 10 minutes to resolve the problem. The distribution of this support time follows the uniform distribution.

a. What are the values for a and b in minutes?

b. What is the mean time to resolve the problem? What is the standard deviation of the time?

c. What percent of the problems take more than 5 minutes to resolve.

d. Supposed we wish to find the middle 50 percent of the problem-solving times. What are the end points of these two times?

4. Compute the mean and variance of the following discrete probability distribution.

x P(x)

2 0.5

8 0.3

10 0.2

5. The director of admissions at Kinzua University on Nova Scotia estimated the distribution of student admissions for the fall semester on the basis of past experience. What is the expected number of admissions for the fall semester? Compute the variance and the standard deviation of the number of admissions.

Admissions Probability

1,000 0.6

1,200 0.3

1,500 0.1

6. According to the insurance institute of America, a family of four spends between $400 and $3,800 per year on all types of insurance. Suppose the money spent is uniformity distributed between these amounts.

a. What is the mean amount spent on insurance?

b. What is the standard deviation of the amount spent?

c. If we select a family at random, what is the probability they spend less than $2,000 per year on insurance per year?

d. What is the probability a family spends more than $3,000 per year?

#### Solution Preview

Probability Exclusive

1. The events A and B are mutually exclusive. Suppose P(A) = .30 and P(B) = .20. What is the probability of either A or B occurring? What is the probability that neither A nor B will happen?

Solution:

Since given that A and B are mutually exclusive events then

Also P(A) = 0.3 and P(B) = 0.2

Then probability of either A or B occurring

P(A U B) = P(A) + P(B) -

= P(A) + P(B)

= 0.3 + 0.2 = 0.5

the probability of neither A nor B will happen

2. A study by the National Park Service revealed that 50% of vacationers going to the Rocky Mountain region visit Yellowstone Park, 40 percent visit the Tetons, and 35 percent visit both.

a. What is the probability a vacationer will visit at least one of these attractions?

b. What is the probability .35 called?

c. Are the events mutually exclusive? Explain.

Sol. Here given that National Park Service revealed that 50% of vacationers going to the Rocky Mountain region visit Yellowstone Park, 40 percent visit the Tetons, and 35 percent visit both.

Let P(A) = probability of ...

#### Solution Summary

The solution examines probability exclusive events.