MATH 106 QUIZ 5

1. (14 pts) There are two coin purses. The first coin purse contains a quarter Q and a nickel N.
The second coin purse contains a dime D and a penny P.
From the first purse a coin is randomly chosen, and from the second purse, a coin is randomly
chosen, and the outcome is recorded. [For instance, the outcome (Q, D) means Quarter from the first
purse and Dime from the second purse.]

(a) List all of the outcomes in the sample space.
(b) Let A be the event "the sum of the coin values is an even number of cents."
What outcomes belong to event A? (Just list them).
What is the probability of event A? ______
(c) Let B be the event "the sum of the coin values is less than 10 cents or greater than 30 cents."
What outcomes belong to event B? (Just list them).
What is the probability of event B? ______
(d) Determine the probability P(A ∪ B), where A and B are the events described above. Show
work/explanation.

2. (6 pts) The probability that a particular baseball team wins its next game is 3/7. What are the
odds for the team winning it next game? What are the odds against the team winning its next
game?

3. (16 pts) A collection of 13 greeting cards consists of 8 birthday cards and 5 thank-you cards.
7 of the cards are randomly selected for purchase.
What is the probability that the 7 purchased cards consist of 4 birthday cards and 3 thank-you
cards? Show work/explanation.
4. (15 pts) For a certain game of chance, a player loses $5 with a probability of 0.30, breaks even with
probability 0.20, gains $1 with probability 0.25, gains $2 with probability 0.15, and gains $6 with
probability 0.10. This information is summarized in the table below (extra space provided for
computations.)
xi
pi

Payoff Table
–$5
$0
0.30
0.20

$1
0.25

$2
0.15

$6
0.10

(a) A player plays this game of chance one time. What is the probability that the player will win some
money? Show work/explanation.

(b) If the player plays the game many times, what is the player’s expectation? That is, what is the
expected value of the probability distribution? Is this a fair game?
Show work. (You are welcome to use the extra row and/or column in the table to make it easier to carry
out the computation.)
5. (25 pts) Medicines to relieve headache pain include Drug X and Drug Y. A study was carried out,
tracking 100 patients suffering from a particular kind of headache, migraine headaches. Each patient was
treated for two migraine headaches. For one migraine headache, Drug X was administered, and for the
other, Drug Y was administered. Given a randomly selected patient, the study found that Drug X relieved
a migraine headache for 40 of the patients, Drug Y relieved a migraine headache for 56 patients, and
Drugs X and Y both relieved the migraine headaches for 24 patients.

(a) Let X = “Drug X relieved migraine” and Y = “Drug Y relieved migraine”. Complete the
following Venn diagram, filling in the appropriate number of patients in each of the regions.

(b) Let event X = “Drug X relieved migraine” and event Y = “Drug Y relieved migraine”. Fill in
the associated probability table with the appropriate probabilities (No work/explanation required)
Y

Y

Totals

X
X
Totals

(d) Given a randomly selected patient, state the probability that Drug X or Drug Y (or both) relieved a
migraine headache.
(c) Given a randomly selected patient, state the probability that Drug Y did not relieve the migraine
headache.

(e) Given a randomly selected patient, state the probability that Drug X relieved a migraine headache but
Drug Y did not.
(f) Given a randomly selected patient, state the probability that neither Drug X nor Drug Y relieved a
migraine headache.

6. (24 pts) The table below gives the distribution of blood types by sex in a group of 600 individuals.
Blood 

Female

Male

Total

Type
O

120

180

300

A

20

162

182

B

12

72

84

AB

8

26

34

160

440

600

Total

(Answers for parts a through f can be stated as fractions, such as 35/46, or as decimals rounded to three
decimal places)

A person is selected at random from the group.
What is the probability that the person:
(a) is male?
(b) has blood type O?
(c) is a male having blood type O?

(d) is a male or has blood type O?

(e) is male, given that the person’s blood type is O?

(f) has blood type O, given that the person is male?

Consider the events M = "person is male" and O = "person has blood type O".

(g) Are the events M and O independent? Explain carefully.