REVIEW
MATH 166:503
April 30, 2015
The final exam covers sections L.1-L.2, 1.1-1.7, 2.1-2.4, 3.1-3.4, F.1-F.4, 4.3-4.4, 5.1-5.3, M.1M.3. Disclaimer: the distribution of problems covered in this review are not indicative of the
distribution on the test but merely serve as extra practice with problems.
1. Decide which of the following are statements:
a. x + 3 = 1
b. Math is fun!
c. 64 − 34 = 5
d. Grass is orange.
2. Write the truth table for p ∨ (∼ q ∧ r).
3. Let the universal set U = {a, b, c, d, e} with sets A = {a, b} and B = {b, c, d}. Consider the
set A ∪ B c . Determine which of the following sets are disjoint to the above set.
a. B
b. Ac ∩ B
c. Ac
d. ∅
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4. List all the subsets of {1, 23, 9}.
5. Write the set that represents the shaded portion of the Venn diagram.
6. Frank’s refrigerator contains 1 Dr. Pepper, 6 Pepsis, and 8 Cokes. If he pulls out three drinks,
without replacement, what is the probability that all the drinks will be the same brand?
7. A bowl contains 9 red marbles, 1 green marble, and 5 purple marbles. An experiment is to
pick a marble and observe it’s color. Is this a uniform sample space? Why or why not?
If not, describe an experiment which has a uniform sample space.
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8. At a volunteer event, boxes lunches containing either an orange or an apple are passed out.
12 boxes contain an orange. 9 boxes contain an apple. If the second person to grab a lunch
box got an apple, what is the probability that the fourth person gets an apple?
If the fifth person gets an orange and the second person gets an apple, what is the probability
that the fourth person gets an apple?
What is the probability that the third or fourth person gets an apple if the first person got
an apple?
9. What is the probability of getting a full house in poker if a full house contains three cards
of matching rank and two other cards of matching rank different than the rank of the first
three?
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10. How many ways can 5 people sit in a row?
How many ways can 5 siblings (none of them twins) be seated in increasing age from left to
right?
11. At a volunteer event, boxes lunches containing either an orange or an apple are passed out.
12 boxes contain an orange. 9 boxes contain an apple. 16 volunteers take the lunches. What
is the probability that at least 3 volunteers get an apple?
What is the expected number of apples?
Let X be the random variable corresponding to the number of apples given to volunteers.
What is σ(X)?
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12. The diameter of basketballs is normally distributed with a mean of 9.7 inches with a standard
deviation of .25 inches. If we bought 350 basketballs, approximately how many do we expect
to have a diameter between 9.4 inches and 10.2 inches?
13. Assume that all 3-digit combinations are allowed in area codes. Let X be the random variable
corresponding to the number of even digits in the area codes. Compute the probability
distribution of X.
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