PROBABILITY
1. In the first session to see if you have ESP, the psychologist has 20 cards with the numbers
1 to 20 written on them.
(a) How many different combinations of cards is possible if she holds 4 cards up facing her
and one at a time, you have to write down the numbers that she is looking at in order?
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(b) How many different combinations are there if she just pulls 4 cards out and you have
to “guess” what four she pulled out?
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2. Can you come up with other situations where order doesn’t matter? Does matter?
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3. Common sources of caffeine in the morning are coffee, tea, and soda drinks. Suppose
that in our school
55% drink coffee (C) ? Lc
25% drink tea (T)
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45% drink soda (S)
You also learn that
15% drink both coffee and tea
5% drink all three beverages
25% drink both coffee and soda
5% drink only tea ?
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Draw a Venn diagram marked with this information labeling each spot with the proper
notation.
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(a) What percent drink none of these beverages?
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(b) Find the P(C U T) using the formula. Check by using the Venn Diagram.
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4. State examples of sets that are mutually exclusive; that are not mutually exclusive.
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7. The probability that a student will eat pretzels (Pr) in study hail is 0.20. The probability a
student will drink a soda (5) in study hail is 0.60. Find P(Pr U S) if:
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(a) Eating pretzels and drinking soda is mutually exclusive from each other
(b) P(Pr fl S)
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(c) Are eating pretzels and drinking soda independent from each other?
8. MusIc styles other than rock and pop are becoming more popular. A survey of college
students finds
country music, and 10% like both.
(a) What is the probability that a student likes country music if we know that he or she
likes hip hop music?
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(b) What is the probability that a student does not like hip hop if we know that he or she
likes country music?
(c) Are the events liking hip hop and liking country music independent from each other?
Show by using math!!
c)
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9. A recent survey suggests that 85% of college students have posted a profile on Facebook,
nd 42% do both
54% use
(a) Are being on Facebook and MySpace independent from each other?
(b) Suppose we select a college student at random and learn that the student has a
Facebook. Find the probability that the student uses MySpace regularly.
10. If 2 events are independent, show they caWt be mutually exclusive.
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11.78% of suspect drivers get a breath test, 36% a blood test, and 22% both. Are giving a
DWI suspect a blood test and a breath test mutually exclusive? Are giving the two tests
independent from each other?
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10. Over 10,000 athletes competed in the 2008 Olympic Games in Beijing. The International
Olympic Committee wanted to endure that the competition was as fair as possible. So the
committee administered more than 5000 drug tests to athletes. All medal winners were
tested, as well as other randomly selected competitors.
% of athletes had actually taken banned drugs. No drug test is perfect.
Suppose that 2
Sometimes the test says that the athlete took the drugs, when they really didn’t. We call
this a false positive result. Other times, the drug test says an athlete is “clean”, but the
athlete actually took drugs. This is called a false negative. Suppose that the testing
procedure used at the Olympics has a false positive rate of 1% and a false negative rate
of 0.5%.
(a) What is the probability that an athlete tests positive on the test?
(b) What is the probability that an athlete who tests positive actually took the drugs?
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11. A computer company, HackerAway, has manufacturing plants in three states: 50% of
their computers are manufactured in New Jersey with 85% desktops, 30% of computers
are made in Delaware with 40% laptops, and the rest is manufactured in Pennsylvania
with 40% of them desktops. All computers are first shipped to a distribution site in
New York before being sent out to stores. If you picked a computer at random from the
NY distribution center, what is the probability that it is a laptop? You just bought a laptop
from HackerAway and then find out that they found a glitch in their laptops produced in
PA. What is the chance that yours has a glitch?
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12. A bridal magazine wants information regarding college students’ attitudes about wedding
costs. Students from a large college campus are randomly selected to take part in a
survey. Students who respond yes to the question, “Do you plan to marry some day?” are
then asked how much they plan to spend on their wedding. The results of the survey are
summarized below.
TOTAL
-.._.COST
<$20,000
$20,000>$50,000
GENDER
$50,000
72
FEMALE
120
197
5
5
175
MALE
147
23
77
372
143
TOTAL
152
Answer the following by first writing the proper notation. Choose a person at random,
(a) What is the probability that the person you choose is a female?
(b) What is the probability that it is a man?
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(c) What is the probability that you choose a female, given that the person chosen would
want to spend $20,000 to $50,000 for their wedding?
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Cd) What is the probability that the person chosen wants to spend under $20,000, given
that he is a man?
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(e) Are the events “choose a gender” and “choose a cost” independent?
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(f) Find the probability of choosing a male who wants a wedding <$20,000 from the
table of counts above.
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(g) Confirm your answer to (f) by using the multiplication rule to find the probability of
choosing a male who wants a wedding < $20,000.