MATH 107
Practice Test #3 -Chapter 7(Sec. A-C,E)
1. Among 20 teachers in a mathematics department, students give prizes to the best teacher and
the worst teacher. In how many ways can the prizes be awarded?
2. There are 10 teams in a conference. If each team is to play every other team exactly once, how
many games must be scheduled?
3. If two dice are rolled, find the following:
a) How many ways can you get a sum of six?
b) How many ways can you get a sum of at least 6?
c) How many ways can you get a different number on each dice?
4. How many five-card poker hands consisting of 3 kings and 2 queens are possible?
5. Evaluate:
a)
6!
0!
b)
100!
98!
c)
7!
3!4!
6. Your history teacher gives you a list of 70 books and informs you that you must read any 3 and
prepare reports on them. How many different selections are possible?
7. If Jill has 3 pairs of pants(red,black,brown), 2 shirts and 3 pairs of shoes (assuming all pants, shirts
and shoes can be worn together), how many different outfits (outfit is a pair of pants, a shirt and a pair
of shoes):
a) are possible?
b) include the red pants?
8. How many five-card poker hands consisting of all hearts is possible?
9. Make a probability distribution for the sums that appear when two fair six-sided dice are tossed.
10. A superintendent of education has twelve schools in her district and wishes to visit four of the
schools.
a) How many different ways are there for her to pick a group of four schools to visit?
b) Once she selected the four schools to visit, how many possible routes are there for her to visit
the four selected schools?
11. A certain model of pickup truck is available in 5 exterior colors, 3 interior colors and 3 interior styles.
In addition, the transmission may be either manual or automatic, and the truck may have either twowheel or four-wheel drive.
a) How many different versions of the pickup may be ordered?
b) How many different versions of the pickup may be ordered if you request a four-wheel drive
automatic?
12. A group of 8 women and 6 men must select a 4-person committee.
a) How many different committees are possible if it must consist of a majority of women?
b) How many committees are possible if it must consist of exactly 2 men and 2 women?
c) What is the probability of randomly selecting a committee of exactly 2 men and 2 women?
13. If you draw a single card from a standard 52-card deck, in how many ways can you get a card that is
a) not a face card?
b) a face card or a black card?
14. Using a standard 52-card deck, how many 5-card poker hands would contain at least one diamond?
15. What is the probability that a 85% free throw shooter will miss his next free throw?
16. If a couple decides to have three children, how many different orders are possible for the couple’s
three children(i.e. boy, boy, boy or BBB)? Name all the possible birth orders.
17. Telephone area codes are three-digit numbers of the form XXX.
a) Originally, the first and third digits were neither 0 or 1 and the second digit was always a 0 or
1. How many three-digit numbers of this type are possible?
b) Over time, the restrictions listed in part a) have been altered, currently, the only requirement is
that the first digit is neither 0 or 1. How many three-digit numbers of this type are possible?
c) Why were the original restrictions listed in part a) altered?
18. How many five-card poker hands consisting of the same suit are possible?
19. Suppose 6 female and 5 male applicants have been successfully screened for 5 positions. If the 5
positions are selected at random from the 11 finalists, what is the probability of selecting:
a) 3 females and 2 males?
b) all females?
c) at least one female?
20. Two coins are tossed.
a) Write the sample space for the given experiment.
b) Write the possible outcomes for the event, F, which is getting at least one head.
c) Find P(F).
d) Find the odds against F.
21. A jar contains 22 red, 18 black, 14 white, 17 green and 10 yellow jellybeans. One jellybean is
chosen at random.
a) Find the probability of white or red.
b) Find the probability of not yellow.
c) Find the odds in favor of selecting red.
22. An experiment consists of dealing 5 cards from a standard 52-card deck. What is the probability of
being dealt:
a) 4 aces?
b) all the same suit?
23. In a hat are placed 10 slips of paper numbered from 1 to 10. You reach in and randomly grab one
slip of paper. What is the probability that you have….
a) an even number?
b) a multiple of 3?
c) an even multiple of 3?
24. Greg has a .78 chance of making par on each hole of golf that he plays. Today he plans to play just
three holes. Find the probability of each event. Round answers to three significant figures.
a) He makes par on all three holes.
b) He makes par on exactly two of the three holes.
c) He makes par on at least one of the three holes.
d) He makes par on the first and third holes but not on the second.
25. A card is dealt from a well-shuffled deck of 52 cards. Find the probability of and the odds of being
dealt a card that is:
a) a black card or a face card.
b) both above a five and below a nine.
c) a red card or a black card.
d) both above a ten and below a four.
26. Suppose a charitable organization decides to raise money by raffling a trip worth $500. If 3,000
tickets are sold at $1.00 each, find the expected net winnings for a person who buys 1 ticket.
27. Two marbles are drawn without replacement from a box with 3 white, 2 green and 1 blue marble.
Find the probability
a) that both marbles are white?
b) that you draw a green and a white marble?
28. In the table below, 500 individuals were classified according to whether or not they owned a bicycle
and also by their sex.
Male
Female
Owns a Bicycle
130
90
Doesn't Own a Bicycle
170
110
What is the probability that a randomly selected individual:
a) owned a bicycle and was female.
b) is male.
c) doesn’t own a bicycle.
29. Before you can drive a car, you must pass a driving test. In a particularly challenging county, 80%
of the applicants pass the first test. Sadly, of those who fail the first test, 20% fail the second test.
What is the probability that a randomly selected individual will fail the test twice?
30. Two cards are dealt from a deck of 52. Find the probability that:
a) the first card is a face card and the second card is an ace.
b) both cards are face cards.
31. The manager of Jack’s baseball team is trying to decide the batting order for the game. There are
15 players on the team and 9 players will be chosen for the batting order. Jack yells, “There are a
billion different batting orders.” Is he right? Justify your answer with math.
32. An insurance company will insure a $220,000 home for its total value for an annual premium of
$510. If the company spends $30 per year to service such a policy, the probability of total loss for
such a home in a given year is 0.001 and you assume either total loss or no loss will occur, what is
the company’s expected annual gain(or profit) on each such policy?
33. It has been determined that the probability of an earthquake occurring on a certain day in a certain
area is 0.05, what are the odds against an earthquake?
34. Andrew and Kevin are playing 5-card poker. Andrew was dealt 3 kings and 2 queens and Kevin
was dealt 4 tens and an ace. Based on probability, who has the better hand?
35. The next test will consist of 5 questions. Each question will be multiple-choice, with 4 possible
solutions listed for each question. What is the probability of an individual correctly answering every
question by guessing?
36. In a fast food store’s lucky number contest, 25% of the customers win $1, 10% win $10, 4% win $20
and 1% wins $50. Find the expected winnings of a customer.
37. A diplomatic delegation of 20 congressional members are categorized as to political party and
gender. Find the probability that a spokesperson for the group could be
a) a Democrat or a man?
Men (M) Women (W)
b) a Democrat and a woman?
c) a female Republican?
Totals
Republican (R)
8
4
12
Democrat (D)
3
5
8
Totals
11
9
20
38. The probability of the horse, Outta Here, winning the 129th Kentucky Derby was 1/50. What were
the actual odds against Outta Here winning the race?
39. What is the probability of randomly meeting someone whose address ends in the same digit as
yours?
40. After recording the forecasts of the local weatherman for 40 days, you conclude that he gave a
correct forecast 18 times. What is the probability that his next forecast will be correct?
Terminology: combinations, factorial, permutations, certain event, event, sample space, outcome,
conditional probability, dependent event, expected value, experiment, impossible event, independent
events, Law of Large Numbers, theoretical probability, experimental (empirical or relative frequency)
probability, mutually exclusive events, odds, probability, Mendel, Cardano, Fermat, Pascal, Laplace,
Pascal’s Triangle
Math 107 Practice Test #3 Answers
Sum
P(Sum)
1.380
2
1/36
2. 45
3
1/18
3. a. 5 b. 26 c. 30
4
1/12
4. 24
5
1/9
5. a. 720 b. 9900 c. 35
6
5/36
6. 54,740
7
1/6
7. a. 18 b. 6
8
5/36
8. 1287
9
1/9
9. see table
10
1/12
10. a. 495 b. 24
11
1/18
11. a. 180 b. 45
12
1/36
12. a. 406 b. 420 c. 0.420
13. a. 40 b. 32
14. 2,023,203
15. 15%
16. 8; BBB, BBG, BGB, GBB, BGG, GBG, GGB, GGG
17. a. 128 b. 800 c. Needed more area codes for a growing population
18. 5148
19. a. 0.433 b. 0.0130 c. 0.998
20. a.
HH ,TH , HT ,TT 
b.
HH ,TH , HT 
c.
3
4
d. 1:3
21.a. 0.444
b. 0.877
c. 22:59
22.a. 0.0000185
b. 0.00198
23.a. 0.5
b. 0.3
c. 0.1
24.a. 0.475
b. 0.402
c. 0.989
d. 0.134
25.a.
8
3
; 8:5 b.
; 3:10
13
13
c. 1; 52:0
d. 0; 0:52
26. -$0.83
27. a. 0.2 b. 0.4
28. a.
9
50
b.
3
5
c.
14
25
29. 0.04
30.a. 0.0181
b. 0.0498
31. No, there are actually more, it is permutations of 15 choose 9 which is 1,816,214,400.
32. $260
33. 19:1
34. Kevin, because the prob. of getting his
hand is 0.00000154 and Andrew’s prob. is 0.00000923.
35. 1/1024 = 0.000977
36. $2.55
37. a. 0.8 b. 1/4 = 0.25 c. 1/5 = 0.2
38. 49 : 1
39. 1/10 = 0.1
40. 0.45