Download Economic Statistics In-class Practice Probability Problems

Economics 310: Economic Statistics
In-class Practice Probability Problems
1. A sample space, S, yields four simple events, A, B, C, and D, such that P(A) = 0.35,
P(B) = 0.10, and P(C) = 0.25.
a. Find P(D)
b. Find P(C)
c. Find P (A U B)
2. An alarming number of US adults are either overweight or obese. The distinction between
overweight and obese is made on the basis of body mass index (BMI), expressed as
weight/height2. An adult is considered overweight if the BMI is 25 or more but less than 30.
An obese adult will have a BMI of 30 or greater. According to the 2003-3004 National
Health and Nutrition Examination Survey, 34.1% of the adult population in the U.S. is
overweight and 322% is obese. Use this information to answer the following questions.
a. What is the probability that a randomly selected adult is either overweight or
obese?
b. What is the probability that a randomly selected adult is neither overweight nor
obese?
c. Are the events “overweight” and “obese” exhaustive?
d. Are the events “overweight” and “obese” mutually exclusive?
3. According to an online survey Harris Interactive for the job site Career Builder.com, more
than half of IT (information technology) workers say they have fallen asleep at work
(InformationWeek, September 27, 2007). Sixty-four percent of government workers
admitted to falling asleep on the job. Consider the following contingency table that is
representative of the survey results.
Slept
on the
job?
Yes
No
IT Professional (IT)
155
145
Government Professional (G)
256
144
a. Convert the contingency table into a joint probability table.
b. What is the probability that a randomly selected worker is an IT professional?
c. What is the probability that a randomly selected worker slept on the job?
d. If a randomly selected worker slept on the job, what is the probability that they were an IT
professional?
e. If a randomly selected worker is a government professional, what is the probability that they
slept on the job?
f. Is job category independent of whether or not a worker slept on the job?
Professor Sandra Camarena
Bowerman text, 4th edition
Economics 310: Economic Statistics
In-class Practice Probability Problems
Answer Key
1.
Sample space (A, B, C, D)
a.
b.
c.
2. Obesity question
a.
b. Using the complement rule,
c. The events “overweight” and “obese” are not exhaustive. The US adult population
also comprises individuals that are neither overweight nor obese. Furthermore,
.
d. According to the BMI classification, an individual is either “overweight” or “obese”.
As a result, the two events are mutually exclusive.
3. Joint probability table (A slight inconsistency in the totals is due to rounding):
a.
b.
Yes
No
Total
c.
d.
e.
Professor Sandra Camarena
Bowerman text, 4th edition
IT Professional (IT)
0.2214
0.2071
0.4286
Government Professional (G)
0.3657
0.2057
0.5714
Total
0.5871
0.4129
1.00