Probability
1. For the cases listed below, indicate which of the
approaches—classical, relative frequency, or subjective—
you would most likely use to assign probability:
a. The probability that at least one of the eggs in the
dozen you just bought will be cracked.
b. The probability that you win the new Trek mountain bike raffle if you purchased 37 of the 200 tickets sold.
c. The probability that Eminem will make a country
music album.
2. For the cases listed below, indicate which of the
approaches—classical, relative frequency, or subjective—
you would most likely use to assign probability:
a. The probability that your professor will be late to
your next class.
b. The probability that there is intelligent life elsewhere in the universe.
c. The probability that you will be involved in a
“fender-bender” accident sometime this year.
3. For the cases listed below, indicate which of the
approaches—classical, relative frequency, or subjective—
you would most likely use to assign probability:
a. The probability that your new TV will self-destruct
one day after the warranty expires.
b. The probability of being chosen randomly to represent your school at a national education conference.
c. The probability that another member of the Bush
family will be elected president of the US.
d. The probability that a pedestrian will be struck by
a bus this year at the intersection of 5th Ave. and 10th St.
4. The table here shows six stocks traded on either the
New York Stock Exchange (NYSE) or the NASDAQ
Exchange. Also shown is an indication of whether
the stock gained or lost value by the close of the
trading day.
ACM BI-SYS CTI DF China EIX FPI
Exchange NYSE NYSE NAS NAS NYSE NAS
Perform Gain Loss Loss Loss Loss Gain
You plan to randomly choose one stock from the
group. Determine
a. the simple probability of selecting a stock that lost
value (Event A).
b. the simple probability of selecting a NYSE stock
(Event B).
5. Below is a table showing the year-to-year US sales
trends for five auto companies headquartered in the
US and Japan.
Nissan Ford GM Suzuki Honda
HQ Japan US US Japan Japan
Trend Up Down Down Up Down
You plan to randomly choose one company from
the group.
a. Determine the simple probability of randomly
selecting a company whose sales trend was down
(Event A).
b. Determine the simple probability of selecting a
company with a US headquarters (Event B).
6. Your advertising firm has five major clients. The type
of business and the gender of the CEO are listed
below:
Nike Intel Sony GE Gap
Type Apparel Tech Tech Tech Apparel
CEO Male Male Male Female Male
a. Determine the simple probability of randomly
selecting a tech company from the list (Event A).
b. Determine the simple probability of selecting a
company whose CEO is female (Event B).
7. The table below is from Exercise 4. It shows six stocks
traded on either the New York Stock Exchange
(NYSE) or the NASDAQ Exchange. Also shown is an
indication of whether the stock gained or lost value
by the close of a particular trading day.
ACM BI-SYS CTI DF China EIX FPI
Exchange NYSE NYSE NAS NAS NYSE NAS
Perform Gain Loss Loss Loss Loss Gain
You plan to randomly choose one stock from the
group. Find the following probabilities:
a. The conditional probability that the stock selected
lost value, given that the stock is a NASDAQ stock.
b. The conditional probability that the stock is a
NYSE stock, given that the stock gained in value.
8. The table below appeared in Exercise 5. It shows the
year-to-year US sales trends for five auto companies
headquartered in the US and Japan.
Nissan Ford GM Suzuki Honda
HQ Japan US US Japan Japan
Trend UP Down Down Up Down
You plan to randomly choose one company from the
group. Find the following probabilities:
a. The conditional probability that the sales trend is
down for the company, given that the company is
headquartered in Japan.
b. The conditional probability that the company
selected has a US headquarters, given that the
sales trend for the company is down.
9. The table below appeared in Exercise 6. It shows the
type of business and the gender of the CEO for your
firm’s five major clients:
Nike Intel Sony GE Gap
Type Apparel Tech Tech Tech Apparel
CEO Male Male Male Female Male
You plan to randomly choose one company from the
group. Find the following probabilities:
a. The conditional probability that the company
CEO is female, given that the company is a tech
company.
b. The conditional probability that the company is an
apparel company, given that the CEO is male.
10. The table from Exercise 4 is shown below. It indicates
the performance of six stocks on a particular trading
day, together with the exchange on which the stocks
are listed.
ACM BI-SYS CTI DF China EIX FPI
Exchange NYSE NYSE NAS NAS NYSE NAS
Perform Gain Loss Loss Loss Loss Gain
You plan to randomly select a stock. According to the
data in the table, are the events “selecting a stock
that lost value” and “selecting a stock listed on the
NYSE” statistically independent? Show the numbers
to make your case and explain exactly what the numbers are indicating.
11. The table from Exercise 5 is shown below. It indicates
year-to-year US sales trends for five major auto
companies.
Nissan Ford GM Suzuki Honda
HQ Japan US US Japan Japan
Trend Up Down Down Up Down
You plan to randomly select a company. According to
the table, are the events “selecting a company in
which the sales trend is up” and “selecting a company whose headquarters is in Japan” statistically
independent? Show the numbers to make your case.
12. The table below appeared in Exercise 6. It shows the
type of business and the gender of the CEO for your
firm’s five major clients:
Nike Intel Sony GE Gap
Type Apparel Tech Tech Tech Apparel
CEO Male Male Male Female Male
You plan to randomly choose one company from the
group. Are the events “selecting a company with a
female CEO” and “selecting a tech company”
statistically independent? Show the numbers to make
your case.
13. Which of the following pairs of events would seem to
be statistically independent? (Keep in mind that to
truly establish independence, we would need to see
probabilities.)
a. A being a Mixed Martial Arts fan.
B reading Shakespeare.
b. A Microsoft stock increases $2 per share.
B GE stock increases $4 per share.
c. A missing your 6 A.M. flight to Paris on May 14.
B staying up late to watch Weekend at B ernie’s
2 on May 13.
d. A winning the first set of a tennis match.
B winning the second set of the same tennis
match.
14. Which of the following event pairs would seem to be
statistically independent? (Keep in mind that to truly
establish independence, we would need to see
probabilities.)
a. A exercising regularly
B having low blood pressure
b. A playing professional sports
B making a million dollars.
c. A reading at least one book per week
B having a full-time job
d. A having a PayPal account
B having a Facebook account
e. A voting Democrat
B owning a riding lawn mower
f. A studying 12 hours a day
B sleeping 15 hours a day
