Solved by a verified expert :MATH 106 QUIZ 5 Extended Due Date:
Wednesday, February 24, 2016

NAME:_______________________________
I have
completed this assignment myself, working independently and not consulting
anyone except the instructor.

INSTRUCTIONS

·
There
are 6 problems (on 5 pages);some
problems have multiple parts. This quiz is open book and open
notes. This means that you may refer to your textbook, notes, and
online classroom materials, but you must work independently and may not consult
anyone(and confirm this with your submission). You may take as much
time as you wish, provided you turn in your quiz no later than 11:59 PM (US
Eastern Time Zone) Wednesday, February 24, 2016.
·
Show work/explanation.
Answers without any work may earn little, if any, credit.You
may type or write your work in your copy of the quiz, or if you prefer, create
a document containing your work. Scanned work is acceptable also; a single file in pdf format is preferred. In
your document, be sure to include your name and the
assertion of independence of work.
·
If
you have any question, please post it in “Ask the Professor” discussion on LEO
if the answer to your question would benefit others in class; otherwise, please
contact me privately via e-mail.

1. (15 pts) There are two envelopes. The
first envelope contains a $1 bill and a $10 bill. The second envelope contains
a $5 bill and a $50 bill.

From the first envelope a bill is randomly
chosen, and from the second envelope, a bill is randomly chosen, and the outcome
is recorded. [For instance, the outcome (1, 5) means $1
bill from the first envelope and $5 bill from the second envelope.]

(a) List all of the outcomes in the sample
space.

(b) Let A be the event “the sum of the
bill values is an even number of dollars.”

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
bill values is greater than 50 dollars.”

What outcomes belong to event B? (Just list them).

What is the probability of event B?
______

(d) Determine the probability P(AÈ B), where A and B are the events described above. Show
work/explanation.

2. (12)A telemarketing executive has determined that
for a particular product, 25% of the people contacted will purchase the product.
If 10 people are contacted, what is the probability that at most 1 will
buy the product? Show work/explanation.

3. (15 pts) A
collection of 11 greeting cards consists of 7 birthday cards and 4 thank-you
cards. Four of the cards are randomly selected for purchase.
What is
the probability that the 4 purchased cards consist of 2 birthday cards and 2
thank-you cards? Show
work/explanation.
(The Answer can be stated as fraction, such as 35/46,
or as decimal rounded to three decimal places)

4. (13 pts) For a certain game
of chance, a player loses $10 with a probability of 0.30, breaks even with probability
0.10, gains $3 with probability 0.20, gains $4 with probability 0.25, and gains
$6 with probability 0.15. This information is summarized in the table below (extra
space provided for computations.)

Payoff Table

xi

–$10

$0

$3

$4

$6

pi

0.30

0.10

0.20

0.25

0.15

(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?
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. (24 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 57 of the patients, Drug Y
relieved a migraine headache for 50 patients, and Drugs X and Y both relieved
the migraine headaches for 24 patients.

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

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

Y

Totals

X

Totals

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

(f) Given a
randomly selected patient, state the probability that neither Drug X nor Drug Y
relieved a migraine headache.

6. (21 pts)The table below gives the distribution of blood
types by sex in a group of 600 individuals.

Blood Type

Male

Female

Total

O

100

208

308

A

34

142

176

B

20

72

92

AB

6

18

24

Total

160

440

600

(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.
Showing
your work, what is the probability that the
person:

(a) is female?

(b) has blood type A?

(c) is a female having blood type A?

(d) is a female or has blood type A?

(e) is female, given that
the person’s blood type is A?

(f) has blood type A, given that the person is female?

Consider the events F = “person is female” and A = “person
has blood type A”.
(g) Are the events F and A independent? Show
work/explain carefully.