Math 1324 Test 3 Review
Test instructions
Time: 90 minutes
What is covered? Section 7.1, 7.2-7.5, 8.1-8.5
Number of questions: 20 Free Response Questions (some questions have sub-questions)
Please show your work neatly. Do not skip steps.
You can use a graphing calculator on Test 3.
Remember the make-up policy: NO MAKE UPS!
1. Given the sets
U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}
A = {2, 3, 4, 10, 11, 15}
B = {1, 5, 9, 10, 11, 12, 13}
Determine the set (A ∩ B ′ ).
Math 1324 – Test 2 Review
Page 1
2. A group of students were surveyed. One-hundred fifty-four are enrolled in Chemistry, 49 are
enrolled in Business Calculus, 38 are enrolled in both, and 26 are not enrolled in either course.
(a) How many students were surveyed?
(b) How many students are enrolled in exactly one of the two courses mentioned here?
(c) How many students are enrolled in Business Calculus or Chemistry?
Math 1324 – Test 2 Review
Page 2
3. Given the following Venn diagram, find 𝑛(E ∪ F ′ )
4. A license plate consists of 2 letters followed by 4 digits. How many license plates are
possible if the 1st letter can’t be O, and no repetition of letters or digits is allowed?
5. A restaurant offers 6 appetizers, 4 salads, 8 entrees, and 5 desserts. In how many ways can a
customer select a meal consisting of an appetizer, a salad, an entrée, and a dessert?
Math 1324 – Test 2 Review
Page 3
6. The company, HEWERRTT, would like letter codes using all of letters in the word
HEWERRTT. How many codes can be made from all the letters in this word?
7. In how many ways can a president, vice-president and a secretary be chosen from 22
members of a club, if one person cannot hold more than one position and all 22 members are
eligible for any position?
8. A committee consists of 11 people. In how many ways can a subcommittee of 4 people be
chosen?
Math 1324 – Test 2 Review
Page 4
9. A coin is tossed 20 times.
(a) How many outcomes are possible?
(b) In how many outcomes do 10 tails occur?
(c) In how many outcomes do at least 18 tails occur?
(d) In how many outcomes do at most 17 tails occur?
Math 1324 – Test 2 Review
Page 5
10. A crate of 17 apples contains 4 rotten apples. Seven apples are chosen at random from the
crate.
(a) How many selections contain 2 rotten and 5 good apples?
(b) How many selections contain 3 rotten apples?
(c) How many selections contain at least 3 rotten apples?
(d) How many selections contain at least 1 rotten apple?
Math 1324 – Test 2 Review
Page 6
11. Let E and F be events of a sample space S. Let P(E′) = 0.69, P(F) = 0.36 and
P(E ∪ F)′ = 0.45. Find each of the following.
(a) P(E ∪ F)
(b) P(E ∩ F)′
(c) P(E ∩ F′)
Math 1324 – Test 2 Review
Page 7
12. A coin is tossed 10 times.
(a) Find the probability that exactly 2 heads occur.
(b) Find the probability that at most 1 head occurs.
(c) Find the probability that at least 3 tails occur.
Math 1324 – Test 2 Review
Page 8
13. A judge has a jury pool of 40 people that contains 22 women and 18 men. She needs a jury
of 12 people.
(a) What is the probability that the jury contains 6 women and 6 men?
(b) What is the probability that the jury contains 8 women?
(c) What is the probability that at most 10 men are on the jury?
(d) What is the probability that at least 11 women are on the jury?
Math 1324 – Test 2 Review
Page 9
14. Let E and F two events with 𝑃(𝐸) = 0.3, 𝑃(𝐹 ) = 0.2 and 𝑃(𝐸 ∪ 𝐹) = 0.35. Find the
following.
(a) 𝑃(𝐸 |𝐹).
(b) 𝑃(𝐸 |𝐹′)
(c) 𝑃(𝐸′ |𝐹)
Math 1324 – Test 2 Review
Page 10
15. Companies A, B. and C produce 10%, 40% and 50% respectively of a certain product. It
has been found that 1 % from A, 1.5 % from B and 2% from C are defective. One of these
products is chosen at random. Find the probability that it produced by Company C, given it was
defective.
16. Urn 1 contains 30 blue and 20 green marbles. Urn 2 contains 20 blue and 25 green marbles.
An urn is chosen at random with equally likely probability, then a marble is chosen.
(a) What is the probability that the marble chosen was green?
(b) What is the probability Urn 1 was chosen, given the marble was green?
Math 1324 – Test 2 Review
Page 11
17. Two cards are drawn without replacement from a well-shuffled deck of 52 playing cards.
What is the probability that the first card drawn is a 6 and the second card drawn is a 7?
18. 10 black balls and 5 white balls are placed in an urn. Two ball are then drawn in succession.
What is the probability that the second ball is white without replacing the first ball?
Math 1324 – Test 2 Review
Page 12
19. A 45-point quiz was given to a history class. The scores are listed below with the
corresponding probability.
X
P(X = 𝑥)
30
32
33
0.15
0.225
0.175
37
42
𝑘
0.1
(a) Find 𝑘.
(b) Find the average for this class.
20. Consider the following binomial experiment: A newspaper publisher claims that 77% of the
people in a certain community read his newspaper. Doubting the assertion, a competitor surveys
281 people in the community. Find the expected value of this experiment if the newspaper
publisher’s claim is correct.
Math 1324 – Test 2 Review
Page 13
20. Consider the following binomial experiment. The probability that a person will get a cold
this winter is 0.55. Ten people are chosen random.
(a) Find the probability that is at least 6 people will get a cold.
(b) Find the probability that is exactly 5 people will get a cold. (Write the formula as well)
(c) Find the probability that at most 3 people will get a cold.
Math 1324 – Test 2 Review
Page 14