NEW
Font size
S
M
L
XL
WorksheetsBasic Probability and Counting
Total questions: 50
Worksheet time: 5hrs 14mins
Name
Class
Date
1.
How many ways can a club select a president, vice president, and a secretary from a group of 5 people?
a)
12
b)
60
c)
15
2.
Homecoming has 7 candidates for King. How many ways can a King and a First Runner-up be chosen to form the Festival Court?
a)
23
b)
840
c)
42
d)
3,628,800
3.
Picking a President, Vice-President, and Secretary from a group of 12.
a)
Permutation
b)
Combination
4.
What is the value of 5!
a)
25
b)
15
c)
120
d)
720
5.
9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
a)
45
b)
362,880
c)
90
6.
How many ways ways can you arrange the letters in the word math?
a)
15
b)
4
c)
24
7.
What does the P stand for in nPr?
a)
Partners
b)
Positions
c)
Papers
d)
Permutations
8.
Determine whether the following scenarios are a permutation or a combination:
Selecting a lead and an understudy for a school play.
Selecting a lead and an understudy for a school play.
a)
Combination
b)
Permutation
9.
Choosing 3 toppings for your sundae out of a list of 15.
a)
Permutation
b)
Combination
c)
Neither
10.
In how many ways can 3 different vases be arranged on a tray?
a)
3
b)
9
c)
6
d)
12
11.
7P2
a)
0
b)
7
c)
42
d)
210
12.
Sarah plays softball over the summer. If there are 10 players on the team, how many ways can the coach make a batting order that includes all players?
a)
1
b)
3628800
c)
100
d)
1814400
13.
The word "arrange" usually refers to
a)
Permutation
b)
Combination
c)
Probability
d)
Counting
14.
The word "selection" usually refers to
a)
Combination
b)
Permutation
c)
Probability
d)
Counting
15.
Permutation is the situation when
a)
A different result occurs when positions of objects are switched
b)
The same result occurs when positions of objects are switched
c)
counting principles are applied
d)
I don't know
16.
When do we use the formula "nPr"?
a)
Permutation. All objects distinct
b)
Permutation. Some identical objects
c)
Arranging people in a row
d)
Forming a group of r objects
17.
Suppose I have the alphabets "A,A,B,B,B,C,D,D,E". When applying "nCr", n = ____ ?
a)
5
b)
9
c)
3
d)
7
18.
Which best describes the "complement" method?
a)
Number of ways in general - Number of ways opposite from question
b)
Number of ways opposite from question
c)
Forming cases
d)
Insert objects in between 2 other objects
19.
I want to arrange 5 people in a row out of a class of 10 people. Number of ways =
a)
10P5
b)
10C5
c)
10!/(5!)
d)
10!-5!
20.
I want to arrange the letters A,A,A,B,B,C,D,E in a row with same alphabets together. Which of the following is the working for the number of arrangements?
a)
5!*3!*2!
b)
8!/(3!*2!)
c)
8!
d)
5!
21.
I want to arrange 5 boys and 5 girls together such that the same gender are together. The number of ways =
a)
2!*5!*5!
b)
2!
c)
10!
d)
10!-(5!*5!)
22.
I have 5 boys and 5 girls. I want to form a team of 4 people with less than 2 boys. Which of the following are the correct case(s)?
a)
0B 4G, 1B 3G, 2B 2G
b)
2B 2G, 3B 1G, 4B 0G
c)
0B 4G, 1B 3G
d)
2B 2G
23.
If A = {1, 3, 5, 7, 9} and B = {2, 3, 5, 7}, what is A ∩ B?
a)
{3, 5, 7}
b)
{2, 3, 5, 7}
c)
{2, 3, 5, 7, 9}
d)
{1, 2, 3, 5, 7, 9}
24.
If A = {1, 3, 5, 7, 9} and B = {2, 3, 5, 7}, what is A ∪ B?
a)
{3, 5, 7}
b)
{2, 3, 5, 7}
c)
{2, 3, 5, 7, 9}
d)
{1, 2, 3, 5, 7, 9}
25.
The Universal Set = { -4, 3, -2, -1, 0, 1, 2, 3 ,4} and A = {0}.
What is the complement of A?
What is the complement of A?
a)
{-4, -3, -2, -1, 0, 1, 2, 3}
b)
{-3, -2, -1, 1, 2, 3}
c)
{-4, -3, -2, -1, 1, 2, 3, 4}
d)
{-4, -3, -2, -1, 1, 2, 3}
26.
If
P = {0, 1, 2, 3, 4}, Q = {4, 6, 8}
R = {6, 12, 18} Then what is (P ∩ Q) ∪ (Q ∩ R)?
P = {0, 1, 2, 3, 4}, Q = {4, 6, 8}
R = {6, 12, 18} Then what is (P ∩ Q) ∪ (Q ∩ R)?
a)
{4}
b)
{4, 6}
c)
{4, 6, 8}
d)
{1, 2, 3, 4, 6, 8}
27.
If
A = {1, 3, 5, 15},
B = {2, 3, 5, 7}
C = {2, 4, 6, 8}
then what is (A U B) ∩ C ?
A = {1, 3, 5, 15},
B = {2, 3, 5, 7}
C = {2, 4, 6, 8}
then what is (A U B) ∩ C ?
a)
{1,3,5}
b)
{1,2,3}
c)
{2,3,5}
d)
{2}
28.
From the above Venn diagram, what is the set S ∩ T?
a)
{casey, drew, jade, glen}
b)
{alex, casey, drew,hunter}
c)
{casey, drew}
d)
{drew, jade}
29.
From the above Venn diagram, what is the set (S ∪ T) ∩ V?
a)
{casey, drew, jade, glen}
b)
{alex, glen, hunter, jade}
c)
{casey, drew, glen}
d)
{drew, jade}
30.
From the above Venn diagram, what is the set S' ? Look at ALL of the Universal set called "U."
a)
{casey, drew}
b)
{blair, francis, glen, jade}
c)
{blair, erin, francis, ira}
d)
{jade, glen, blair, erin, francis, ira}
31.
How many students do not ski or ice skate?
a)
10
b)
16
c)
22
d)
28
32.
How many students do not snowboard?
a)
21
b)
22
c)
28
d)
29
33.
What does the shaded region of the Venn diagram represent?
a)
P or S
b)
Only P or S
c)
P and S
d)
Only P and S
34.
What statement does the shaded region represent?
a)
A and B and C
b)
A or B and C
c)
B and C
d)
A or C
35.
What statement does the shaded region represent?
a)
A or B and C
b)
Not C
c)
A or B
d)
B and C or A
36.
What is the answer to the question in the image?
a)
18
b)
20
c)
29
d)
25
37.
A bag contains 30 pieces of candy. There are 15 grape, 7 cherry, 3 lemon, 5 strawberry. What is the probability of drawing a lemon?
a)
3
b)
1/10
c)
3/10
d)
30%
38.
The probability of an event occurring, P(A), can be expressed as a fraction, decimal, or percent.
a)
True
b)
False
39.
If an event has a probability of 0, then it is...
a)
impossible
b)
certain
c)
equally likely as unlikely
d)
small chance
40.
If an event has a probability of 1, then it is...
a)
impossible
b)
certain
c)
equally likely as unlikely
d)
very close to certain.
41.
If two Events A and B are independent in relation, then P(B|A) =
a)
P(B)
b)
P(A)
c)
P(A|B)
d)
P(A and B)
42.
Two Events that have no outcomes in common are called...
a)
Disjoint (Mutually Exclusive)
b)
Overlapping
c)
Independent
d)
Dependent
43.
This type of probability involves collecting data in the real word
a)
Experimental (Empirical)
b)
Theoretical (Classical)
c)
Subjective
d)
None of these
44.
What is the probability that a person selected at random from this data set drives a sports car, given that they are female?
a)
25%
b)
53.6%
c)
18.8%
d)
11%
45.
In a room there are five freshmen, three sophomores, four juniors and six seniors.
If you pick two different people from this room at random, what is the probability that they are both juniors?
If you pick two different people from this room at random, what is the probability that they are both juniors?
a)
0.0392
b)
0.0494
c)
0.4444
d)
0.3987
46.
The fire company sells 200 raffle tickets each year, only one of which is the winner.
If you buy a ticket from the fire company every year for the next 10 years, what is the probability that you will win this raffle at least once?
If you buy a ticket from the fire company every year for the next 10 years, what is the probability that you will win this raffle at least once?
a)
0.0489
b)
0.05
c)
0.0951
d)
0.01
47.
There are 13 students in a room. A trial consists of picking four different students at random.
According to the Fundamental Counting Principle, how many outcomes does this trial have, respective of order?
According to the Fundamental Counting Principle, how many outcomes does this trial have, respective of order?
a)
17,160
b)
28,561
c)
52
d)
67,108,864
48.
There is a 7% probability of a major earthquake in Japan this year. If a major earthquake does occur, the probability that there will be another major earthquake next year falls to 5%.
However, if a major earthquake does not occur this year, the probability of a major earthquake next year rises to 9%.
What is the probability that there will be exactly one major earthquake in Japan in the next two years?
However, if a major earthquake does not occur this year, the probability of a major earthquake next year rises to 9%.
What is the probability that there will be exactly one major earthquake in Japan in the next two years?
a)
15.02%
b)
2.04%
c)
86.35%
d)
84.63%
49.
In a room of 21 people, 12 are boys and 9 are girls. What are the odds in favor of picking a boy?
a)
4:3
b)
4:7
c)
3:4
d)
7:4
50.
Probability is ...
a)
the chance that some event will occur.
b)
a game that involves coins.
c)
a guarantee.
Reset
