2. (6 pts) The probability that a particular basketball 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?
There is a 3 out of 7 chance the team will win the next game
There is a 7 out of 3 chance the team will lose the next game
3. (16 pts) A collection of 18 greeting cards consists of 15 birthday cards and 3 thank-you cards.
7 of the cards are randomly selected. What is the probability that the 7 randomly selected cards consist of 5 birthday cards and 2 thank-you notes? Show work/explanation.
4. (15 pts) For a certain game of chance, a player loses $6 with a probability of 0.25, breaks even with probability 0.15, gains $1 with probability 0.40, gains $4 with probability 0.15, and gains $8 with probability 0.05. This information is summarized in the table below (extra space provided for computations.)
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Payoff Table |
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xi |
–$6 |
$0 |
$1 |
$4 |
$8 |
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pi |
0.25 |
0.15 |
0.40 |
0.15 |
0.05 |
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(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.)
(c ) Is this a fair game? Explain.
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 52 of the patients, Drug Y relieved a migraine headache for 66 patients, and Drugs X and Y both relieved the migraine headaches for 40 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)
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X |
X¢ |
Totals |
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Y |
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Y¢ |
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Totals |
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(c) Given a randomly selected patient, state the probability that Drug X or Drug Y relieved a migraine headache.
(d) 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.
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Blood Type |
Male |
Female |
Total |
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O
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100 |
208 |
308 |
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A
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30 |
120 |
150 |
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B
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34 |
72 |
106
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AB
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6 |
30 |
36 |
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Total
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170 |
430 |
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 female?
(b) has blood type A?
(c) is a female and has 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? Explain carefully.
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