# Project #2618 - Exam

1. (14 pts) There are two coin purses. The first coin purse contains a nickel N and a quarter, Q. 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 (N, P) means Nickel from the first purse and Penny 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 È B), where A and B are the events described above. Show work/explanation.

2. (6 pts) The probability that a particular basketball team wins its next game is 4/7. 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 sandwich tray holds 18 sandwiches. 11 of them are ham sandwiches and the other 7 are turkey sandwiches.

8 of the sandwiches are randomly selected by guests at a lunch gathering.

What is the probability that the 8 randomly selected sandwiches consist of 3 ham sandwiches and 5 turkey sandwiches? Show work/explanation.

4. (15 pts)  For a certain game of chance, a player loses \$3 with a probability of 0.40, breaks even with probability 0.15, gains \$1 with probability 0.30, gains \$4 with probability 0.05, and gains \$5 with probability 0.10. This information is summarized in the table below (extra space provided for computations.)

 Payoff  Table xi –\$3 \$0 \$1 \$4 \$5 pi 0.40 0.15 0.30 0.05 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 58 of the patients, Drug Y relieved a migraine headache for 47 patients, and Drugs X and Y both relieved the migraine headaches for 20 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 X 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 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.

What is the probability that the person:

(a) is male?

(b) has blood type B?

(c) is a male having blood type B?

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

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

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

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

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

 Subject Mathematics Due By (Pacific Time) 02/24/2013 11:00 pm
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