# Probability Exclusive Events 1 The events A and B are mutually exclusive Suppose P(A) = 30 and P(B)

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 05

8 03

10 02

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

1,000 06

1,200 03

1,500 01

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?