Question 1

What is the arrangement of n objects in a specified order?

Accepted Answer

Permutation

Answer

Combination

Answer

Operation

Answer

Probability

Question 2

Which of the following illustrates combination?

Accepted Answer

Drawing names from the box for raffle

Answer

Forming plate numbers of a vehicle

Answer

Arranging books in a shelf

Answer

Opening a vault

Question 3

If there are 7 people and only 5 chairs are available, which of the following is the correct illustration of how many ways they can be seated?

Accepted Answer

7x6x5x4x3

Answer

7x6x5x4x3x2x1

Answer

5x7

Answer

7x5

Question 4

How many ways can 5 cotestants be lined up in a stage if two of them insisted to stand together?

Accepted Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Question 5

Which of the following refers to a selection object where order is not important?

Accepted Answer

Combination

Answer

Permutation

Answer

Event

Answer

Sample Space

Question 6

How many ways can four different cars be lined up?

Accepted Answer

24

Answer

16

Answer

32

Answer

8

Question 7

Which of the following illustrates permutation?

Accepted Answer

Assigning LRN among the students

Answer

Choosing a song to play

Answer

Selecting a hero in playing Ragnarok

Answer

Choosing a guest to attend a party

Question 8

A bracelet has 6 different charms. How many arrangements of the charms are possible?

Accepted Answer

60

Answer

5040

Answer

120

Answer

720

Question 9

How many ordered arrangements can be made from the letters in the word PROBABILITY?

Accepted Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Question 10

Which of the following can be the value of n in P(n,5) = 2520?

Accepted Answer

7

Answer

9

Answer

3

Answer

6

Question 11

If C(8,r) = 56, what is the value of r?

Accepted Answer

3

Answer

5

Answer

4

Answer

2

Question 12

John and his 5 friends will attend a dinner gathering. In how many ways they can be seated in a circular table?

Accepted Answer

5!

Answer

4!

Answer

(6!-1!)

Answer

(6!-1)!

Question 13

Evaluate: P (8, 3)

Accepted Answer

336

Answer

40320

Answer

56

Answer

24

Question 14

In how many ways can four cards from a deck of 52 cards be laid face up in a row?

Accepted Answer

P(52, 4)

Answer

P(52, -4)

Answer

P(4, 52)

Answer

P(52, 4)!

Question 15

In a research study, 180 college freshmen were interviewed for their favorite sports. As a result , there were 115 freshmen who like basketball, 67 in volleyball and 38 in both sports.

Find the probability of students who chose only basketball.

Accepted Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Question 16

In a research study, 180 college freshmen were interviewed for their favorite sports. As a result , there were 115 freshmen who like basketball, 67 in volleyball and 38 in both sports.

Find the probability of students who chose only volleyball.

Accepted Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Question 17

In a research study, 180 college freshmen were interviewed for their favorite sports. As a result , there were 115 freshmen who like basketball, 67 in volleyball and 38 in both sports.

Which of the following illustrates the probability of students who chose basketball or volleyball?

Accepted Answer

P(Basketball ∪ Volleyball)

Answer

P(Basketball)

Answer

P(Volleyball)

Answer

P(Basketball ∩ Volleyball)

Question 18

In a research study, 180 college freshmen were interviewed for their favorite sports. As a result , there were 115 freshmen who like basketball, 67 in volleyball and 38 in both sports.

What is the probability of students who chose at least one sport?

Accepted Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Question 19

In a research study, 180 college freshmen were interviewed for their favorite sports. As a result , there were 115 freshmen who like basketball, 67 in volleyball and 38 in both sports.

Determine the probability of students who chose niether of the sports.

Accepted Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Question 20

A single card is chosen at random from a standard deck of 52 playing cards. What is the probability of choosing a card that is not a diamond?

Accepted Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Question 21

Two veteran candidates A and B are running for re-election. If the probability that A will win the election is 0.43, what is the probability that B will win? (Assume that they are the only candidates)

Accepted Answer

0.57

Answer

1.0

Answer

0.43

Answer

0.5

Question 22

What is the probability of drawing a King and Queen from a deck of cards?

Accepted Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

0

Question 23

A jar contains six red marbles, eight white marbles and ten blue marbles. What is the probability of getting a white ball or a red marble on a single draw?

Accepted Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Question 24

What is the probability that a card drawn is ace or a heart

Accepted Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

1

Question 25

In a standard deck of cards, find the probability that a card is drawn is not a heart.

Accepted Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Question 26

Two fair of dice are rolled. What is the probability that the sum is less than 6 occurs?

Accepted Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Question 27

Ruby's dog has 8 puppies which include white females, 3 mixed-color females, 1 white male, and 2 mixed-color males. Ruby wants to keep the puppy. What is the probability that she randomly chooses a puppy that is female or white?

Accepted Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Question 28

If two events, A and B, are mutually exclusive, then which of the following is the probability that either A or B occurs?

Accepted Answer

P(A or B) = P(A) + P(B)

Answer

P(A or B) = P(A) + P(B) - P(AB)

Answer

P(A or B) = P(A) - P(B)

Answer

P(A or B) = P(A) + P(B) - P(AB)

Question 29

How many 3-digit numbers can be formed from the digits 1, 3, 4, 5 and 7 if repetition is not allowed?

Accepted Answer

10

Answer

60

Answer

210

Answer

120

Question 30

From a group of 8 puppies, how many ways can Jackie adapt 3 puppies?

Accepted Answer

56

Answer

112

Answer

8064

Answer

2688

Question 31

A club has 20 members. They wish to elect officers consisting of a President, a Vice President, a Secretary, a treasurer. How many sets of officers are possible?

Accepted Answer

116 280

Answer

80

Answer

29 070

Answer

40

Question 32

In how many ways can four boys and five girls be seated in a row of nine seats if boys and girls are to occupy alternate seats?

Accepted Answer

2880

Answer

120

Answer

20

Answer

24

Question 33

A box contains of 7 honey dipped and 4 bavarian donuts. How many ways can you choose 3 honey dipped and 2 bavarian donuts?

Accepted Answer

210

Answer

41

Answer

222

Answer

2520

Question 34

Evaluate: C (5,5) + P (6,3) - C (8,4)

Accepted Answer

51

Answer

-49

Answer

49

Answer

-1659

Question 35

If friends of 5 attend a party and two of them must sit together, what must be the value of n?

Accepted Answer

4

Answer

1

Answer

5

Answer

2

Question 36

What is the value of $_7C_2$ ?

Accepted Answer

21

Answer

14

Answer

5

Answer

9

Question 37

How many distinguishable arrangements can be made out of the letters of the word PEACE?

Accepted Answer

60

Answer

10

Answer

120

Answer

30

Question 38

In a spinner numberred from 1 to 8, what is the probability of obtaining a 5?

Accepted Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Question 39

Chris Rolled a pair of die. What is the probability of getting an even number divisible by 3?

Accepted Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Question 40

How many students were surveyed?

Accepted Answer

40

Answer

20

Answer

45

Answer

39

Question 41

Use the illustration in the picture.

What is P(I)?

Accepted Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Question 42

Use the illustration in the picture.

What is the union of two events $\left(F\cup T\right)$

Accepted Answer

31

Answer

19

Answer

11

Answer

23

Question 43

Use the illustration in the picture.

What is the intersection of two events $\left(T\cap I\right)$

Accepted Answer

4

Answer

2

Answer

23

Answer

12

Question 44

A bag contains 6 black marbles, 3 blue marbles, 4 pink marbles and 2 violet marbles . A marble is randomly selected, replaced and a second marble is randomly selected. Find the probability of selecting a black marble, then a blue marble?

Accepted Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Question 45

A box of chocolates contains 10 milk chocolates, 8 dark chocolates and 6 white chocolates. Chris randomly chooses a chocolate, eats it then randomly chooses another chocolate. What is the probability that Chris chose both dark chocolates?

Accepted Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Question 46

A school supplies store has 5 red ballpens, 8 black ballpens and 10 blue ballpens. James bought one ballpen but returns it because of defect and gets another pen. Which of the following best describes its probability of events?

Accepted Answer

Independent Events

Answer

Dependent Events

Answer

Mutually Exclusive

Answer

Not Mutually Exclusive

Question 47

What is the probability of getting tails if you flip the coin again?

Accepted Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Question 48

Two light bulbs are drawn at random from 30 light bulbs of which five are defective . What is the probability that both bulbs are working?

Accepted Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Question 49

In a 7-sided spinner, what is the probability of getting an even number or a number less than 5?

Accepted Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Question 50

There are 15 students, 10 boys and 5 girls, in a remedial class. If a committee of 3 students is formed, what is the probability that all are girls?

Accepted Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

Answer

$\left(_4P_4\right)\left(_2P_2\right)$

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