counting

Practice Sheet 01

01550022244
01063579366
1. A bag of jellybeans has 20 watermelon jellybeans, 45 4. If x is chosen at random from the set (4, 6, 7, 9, 11)
sour apple jellybeans, 30 orange jellybeans and 5 cotton and y is chosen at random from the set (12, 13, 15, 17)
candy jellybeans. If you reach in and grab one jellybean, then what is the probability that 𝒙𝒚 is odd?
what is the probability that it will be watermelon 9
a)
flavored? 10

11
a)
1 b)
20
4
6
b)
1 c)
20 10

9
c)
1 d)
5 20

3
d)
4 e)
19 10

e)
1 5. Mike has a bag of marbles, 4 white, 8 blue, and 6 red.
3
He pulls out one marble from the bag and it is red.
2. A circle is inscribed inside a square. If a point inside What is the probability that the second marble he
the square is selected at random, what is the pulls out of the bag is white?
probability that the point will also be inside the circle? 3
a)
𝜋 18
a)
4 1
b)
5 6
b)
6 4
c)
3 17
c)
4 4
d)
𝜋 18
d)
6 4
e)
𝜋 13
e)
2
6. Michael tosses three fair coins. What is the
3. John has a bowl with 54 marbles in it. Half of the probability that at least one of these coins will land
marbles are green, and half of the marbles are blue. on heads?
John takes 3 green marbles and 6 blue marbles from
1
the jar. John then takes 13 additional marbles from the a)
8
remaining marbles in the jar. What is the minimum 3
b)
number of these 13 marbles that must be green for 4

there to be more blue marbles than green marbles left? 1

c)
4
a) 10 1
d)
2
b) 8
7
e)
8
c) 4

d) 5

e) 9

MR. AHMED SAMAK 1

7. A jar of marbles has 125 marbles in it. 25 are blue 10. There is a special contest held at a high school
marbles, 65 are red marble, 15 are green marbles and where the winner will receive a prize of $100. 300
20 are yellow marbles. What is the probability that the seniors, 200 juniors, 200 sophomores, and 100
first three marbles picked are green or blue? freshmen enter the contest. Each senior places
their name in the hat 5 times, juniors 3 times, and
a) 0.025
sophomores and freshmen each only once. What is
b) 0.031 the probability that a junior's name will be chosen?
1
c) 0.015 a)
24

d) 0.020 b)
2
5

e) 0.043 1
c)
6
8. If given two dice, what is the probability that the sum 5
d)
of the two numbers rolled will equal 9? 8

1
a)
1 e)
6 4

b)
1 11. Michelle is randomly drawing cards from a deck
24
of 52 cards. What is the chance she will draw a black
1
c) queen followed by a 5 of any color, without
18
replacing the cards?
1
d)
36 2
a)
1 169
e)
9 8
b)
663
9. A bag contains 6 green marbles, 5 blue, and 9 red.
2
What is the probability that you will select two green c)
2652
marbles from the bag? 4
d)
6 169
a)
20 2
e)
9 663
b)
100
12. There are 5 girls and 4 boys in Homeroom A, and
21
c) 3 boys and 7 girls in Homeroom B. If each
190
homeroom selects one captain at random from
5
d) among its students, what is the probability that a
42

3 boy is selected in at least one of the homerooms?

e)
38
67
a)
90

11
b)
10

12
c)
19

7
d)
18

11
e)
18

MR. AHMED SAMAK 2

13. There are 18 jellybeans in a jar. 6 are red, 7 are 15. If a number is chosen at random from the set {2,
green, and 5 are purple. What is the probability that a 4, 6, ..., 20}, what is the probability that the chosen
jellybean chosen at random from the jar is red or number is divisible by 3?
purple? 1
a)
3
1
a)
3 1
b)
5
2
b)
3 𝑙
c)
6
5
c)
6 3
d)
5
11
d)
18 3
e)
10
13
e)
16. Alec has 2 stacks of cards. The first stack
18

14. The circular region below has 8 sectors of equal contains 5 red cards and 5 black cards. The second
area. Each sector is labeled with a symbol. If a pebble is stack contains 3 red cards, 4 black cards, and 5 blue
dropped randomly onto the region, what is the cards. Alec draws one card at random from each
probability that the pebble will land on a sector whose stack. What is the probability that both cards drawn
label is a star? are black?
1
a)
8

1
b)
6

1
c)
4

1
d)
3

5
e)
6

17. Debbie chooses her outfit for the day from 6

1
a) shirts, 3 pairs of jeans, 2 jackets, and 3 pairs of
8

1 sneakers. How many different outfits are possible if

b)
4 she chooses exactly 1 shirt, 1 pair of jeans, 1 jacket,
3 and 1 pair of sneakers?
c)
8

1 a) 4
d)
2
b) 5
3
e)
4
c) 14

d) 54

e) 108

MR. AHMED SAMAK 3

18. An exam contains 4 questions. Each question has 5 21. In a jar filled with gumballs, 42 are red, 33 are
answer choices. Which of the following expressions purple, and the rest are orange. The probability of
gives the total number of possible answer randomly selecting an orange gumball from the jar
combinations for this exam? 𝟏
is . How many orange gumballs does the jar
𝟔

a) 45 contain?

b) 54 a) 10

c) 4(3)(2) b) 15

d) 5(4) c) 20

e) 5(4)(3)(2) d) 30

19. A pastry shop gives each customer a ticket with a 3- e) 35

digit order number. Each digit must be between 1 and 7, 22. A bag contains 36 cookies: 16 chocolate chip, 8
inclusive, and cannot be repeated in the same order oatmeal, and 12 peanut butter. How many
number. How many different order numbers are additional oatmeal cookies must be added to the
possible? bag so that the probability of randomly selecting an
𝟏
a) 60 oatmeal cookie is ?
𝟑

b) 120 a) 4

c) 210 b) 5

d) 216 c) 6

e) 343 d) 9

20. A box contains b blue marbles and w white marbles. e) 12

If the probability of randomly drawing a white marble
3 𝝎 23. Syed is playing a game that involves rolling a
from the box is what is the value of ?
7 𝒃 standard six-sided dice 6 times. If he rolls each
1 number exactly once, he will win a prize. He has
a)
4
already rolled a "2" and a "5". What is the
b)
1
probability that he will win a prize? (Note: The faces
2
of a standard six-sided dice are numbered from 1 to
2
c) 6.)
3

3 1
d) a)
4 24

4 1
e) b)
3 54

1
c)
120

1
d)
720

3
e)
32

MR. AHMED SAMAK 4

24. How many 3-person committees can be selected 27. In a plane there are 8 points, no three of which
from a fraternity with 25 members? are collinear. How many lines do the points
determine?
a) 15,625
a) 7
b) 13,800
b) 16
c) 2,300
c) 28
d) 75
d) 36
e) 8
e) 64
25. A basketball team has 5 centers, 9 guards, and 13
forwards. Of these, 1 center, 2 guards, and 2 forwards 28. With the throw of two dice, what is the
start a game. How many possible starting teams can a probability that the sum will be a prime number?
coach put on the floor? 4
a)
11
a) 56,160
7
b)
18
b) 14,040
5
c)
c) 585 12

5
d) 197 d)
11

1
e) 27 e)
2

26. Five boys and 6 girls would like to serve on the 29. If a coin is flipped and one die is thrown, what is
homecoming court, which will consist of 2 boys and 2 the probability of getting a head or a 4?
girls. How many different homecoming courts are 1
possible? a)
12

1
a) 30 b)
3

b) 61 c)
5
12

c) 150 7
d)
12
d) 900 2
e)
3
e) 2048

MR. AHMED SAMAK 5

30. Three cards are drawn from an ordinary deck of 52 32. Of all the articles in a box, 80% are satisfactory,
cards. Each card is replaced in the deck before the next while 20% are not. The probability of obtaining
card is drawn. What is the probability that at least one exactly five good items out of eight randomly
of the cards will be a spade? selected articles is.

a)
3
a) 0.003
52

b)
9 b) 0.013
64

3 c) 0.132
c)
8

37
d) 0.147
d)
64
e) 0.8
3
e)
4

31. A class has 12 boys and 4 girls. If three students are

selected at random from the class, what is the
probability that all will be boys?
1
a)
55

1
b)
4

1
c)
3

11
d)
28

11
e)
15

32. A hotel has five single rooms available, for which six
men and three women apply. What is the probability
that the rooms will be rented to three men and two
women?
23
a)
112

97
b)
251

10
c)
21

5
d)
9

5
e)
8

MR. AHMED SAMAK 6

Answers 29- d

1- c 30- d

2- a 31- d

3- e 32- c

4- d 33- d

5- c 34- b

6- d

7- b

8- e

9- e

10- e

11- e

12- e

13- d

14- c

15- e

16- b

17- e

18- b

19- c

20- d

20- b

21- c

22- b

24- c

25- b

26- c

27- c

28- c

MR. AHMED SAMAK 7