Conditional Probability and Independence: Interactive Learning Quizzes

Question 1

Two fair coins are flipped. What's the chance the first coin lands on heads if the second coin lands on tails?

Accepted Answer

1/2

Answer

1/4

Answer

3/4

Question 2

A bag contains 5 red balls and 3 blue balls. If a ball is drawn randomly from the bag, what is the probability that it is blue, given that it is not red?

Accepted Answer

3 / 8

Answer

1 / 8

Answer

5 / 8

Answer

1 / 3

Question 3

A deck of cards contains 52 cards. If two cards are drawn randomly without replacement, what is the probability that the first card is a king and the second card is an ace?

Accepted Answer

1 / 221

Answer

1 / 13

Answer

1 / 52

Answer

1 / 104

Question 4

A bag contains 5 red balls, 3 blue balls, and 2 green balls. If a ball is drawn at random, what is the probability that it is red, given that it is not green?

Accepted Answer

5/8

Answer

1/2

Answer

2/5

Question 5

If P(A) = 0.4 and P(B) = 0.6, what is the probability of the intersection of events A and B?

Accepted Answer

0.24

Answer

0.48

Answer

0.36

Answer

0.16

Question 6

If two events, A and B, are mutually exclusive, then:

Accepted Answer

P(A ∩ B) = 0

Answer

P(B|A) = P(B)

Answer

P(A|B) = P(A)

Question 7

If P(A|B) = 0, then:

Accepted Answer

A and B are mutually exclusive

Answer

A is a subset of B

Answer

A and B are independent

Answer

B is a subset of A

Question 8

Which of the following is NOT an axiom of probability?

Accepted Answer

P(A) can be greater than 1

Answer

P(A) cannot be negative

Answer

If A and B are disjoint, then P(A ∪ B) = P(A) + P(B)

Answer

P(S) = 1

Question 9

Two coins are tossed. What is the probability that the first coin lands on heads and the second coin lands on tails? Assume the tosses are independent.

Accepted Answer

0.25

Answer

0.3

Answer

0.4

Answer

0.5

Question 10

A box contains 5 red balls and 3 blue balls. A ball is drawn at random and replaced. A second ball is then drawn. What is the probability that both balls are red?

Accepted Answer

0.25

Answer

0.4

Answer

0.33

Answer

0.2

Question 11

A bag contains 5 red and 3 blue balls. Two balls are drawn randomly, one after the other, without replacement. What is the probability of drawing a red ball first and then a blue ball?

Accepted Answer

5/24

Answer

3/10

Answer

1/4

Answer

1/3

Question 12

The probability of rolling a head on a coin toss is 1/2. If the coin is tossed twice, what is the probability of rolling a head on the first toss and a tail on the second toss?

Accepted Answer

1/4

Answer

1/16

Answer

1/2

Answer

1/8

Question 13

A box contains 4 red balls and 6 blue balls. If two balls are drawn randomly, with replacement, what is the probability that both balls are blue?

Accepted Answer

9/25

Answer

1/4

Answer

1/2

Answer

1/8

Question 14

A committee of 5 people is to be selected from a group of 8 men and 6 women. If the committee must have at least 3 women, what is the probability that the committee will have exactly 3 women?

Accepted Answer

15/64

Answer

1/4

Answer

1/8

Answer

1/2

Question 15

A company's customer list includes 1000 individuals, of which 600 are male and 400 are female. If 20% of the male customers and 30% of the female customers are over 40 years old, what is the probability of randomly selecting a customer who is over 40 years old?

Accepted Answer

0.26

Answer

0.20

Answer

0.40

Answer

0.30

Question 16

Two events, A and B, are mutually exclusive if:

Accepted Answer

P(A and B) = 0

Answer

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

Answer

P(not A) = P(B)

Answer

P(A|B) = 1

Question 17

If the probability of event A occurring is 0.4, the probability of event B occurring is 0.6, and the probability of both events A and B occurring is 0.2, what is the conditional probability of event A occurring given that event B has already occurred?

Accepted Answer

1/3

Answer

1/4

Answer

1/2

Answer

2/3

Question 18

Two events, A and B, are considered independent if:

Accepted Answer

The occurrence of one event does not affect the probability of the other event.

Answer

The probability of both events occurring is equal to the sum of their individual probabilities.

Answer

The probability of either event occurring is greater than the probability of both events occurring.

Answer

The probability of the complement of one event is equal to the probability of the other event.

Question 19

Two events, A and B, are mutually exclusive if:

Accepted Answer

They cannot both occur at the same time.

Answer

The probability of either event occurring is greater than the probability of both events occurring.

Answer

The probability of both events occurring is equal to the sum of their individual probabilities.

Answer

The probability of the complement of one event is equal to the probability of the other event.

Question 20

The complement of the event "A: rolling a number greater than 4 on a standard six-sided die" is:

Accepted Answer

A': rolling a number less than or equal to 4

Answer

A': rolling a number odd

Answer

A': rolling a number even

Answer

A': rolling a number 6

Question 21

Two events, A and B, are independent if:

Accepted Answer

The occurrence of one event does not affect the probability of the other event occurring.

Answer

The events occur at the same time.

Answer

The events are mutually exclusive.

Question 22

A box contains 6 red balls and 4 blue balls. Two balls are drawn at random without replacement. What is the probability that the first ball is red and the second ball is blue?

Accepted Answer

4/15

Answer

2/5

Answer

1/2

Answer

1/3

Question 23

A survey of 100 students found that 60 students play basketball, 40 students play soccer, and 20 students play both basketball and soccer. What is the probability that a randomly selected student plays basketball or soccer?

Accepted Answer

80/100

Answer

60/100

Answer

40/100

Question 24

A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. If two marbles are drawn at random with replacement, what is the probability that both marbles are blue?

Accepted Answer

9/100

Answer

1/25

Answer

1/4

Answer

1/10

Question 25

Two events, A and B, are mutually exclusive if:

Accepted Answer

They cannot both occur at the same time.

Answer

They are independent.

Answer

They are equally likely to occur.

Answer

They have the same probability.

Question 26

Two events, A and B, are dependent if:

Accepted Answer

The occurrence of one event affects the probability of the other event occurring.

Answer

They have the same probability.

Answer

They are independent.

Question 27

Two events A and B are independent if:

Accepted Answer

The occurrence of event A does not affect the probability of event B.

Answer

The probability of both events occurring is equal to the sum of their individual probabilities.

Answer

The events are mutually exclusive.

Question 28

A coin is tossed twice. What is the probability of getting tails on the first toss and heads on the second toss?

Accepted Answer

1/4

Answer

1/8

Answer

1/2

Answer

1/3

Question 29

A bag contains 6 red balls, 4 blue balls, and 2 green balls. A ball is drawn at random and replaced. What is the probability of drawing a second blue ball?

Accepted Answer

1/3

Answer

2/9

Answer

1/4

Question 30

Two events A and B are mutually exclusive if:

Accepted Answer

They cannot occur at the same time.

Answer

The occurrence of one event affects the probability of the other event.

Answer

The probability of one event occurring is greater than the other event.

Answer

They are independent events.

Question 31

A coin is tossed three times. What is the probability of getting at most two tails?

Accepted Answer

7/8

Answer

1/8

Answer

1/4

Answer

1/2

Question 32

Two events A and B are dependent events if:

Accepted Answer

The occurrence of event A affects the probability of event B.

Answer

They are independent events.

Answer

They cannot occur at the same time.

Question 33

A bag contains 5 red marbles and 3 blue marbles. If one marble is selected at random, what is the probability of picking a red marble?

Accepted Answer

5/8

Answer

3/8

Answer

1/2

Answer

1/4

Question 34

Two events, A and B, are considered independent if:

Accepted Answer

The outcome of one event does not influence the probability of the other event happening.

Answer

The occurrence of one event makes the other event more likely to happen.

Answer

The probability of both events happening is the product of their individual probabilities.

Answer

The occurrence of one event increases the probability of the other event happening.

Question 35

If the probability of event A is 0.4 and the probability of event B is 0.6, what is the probability of event A or event B happening?

Accepted Answer

0.8

Answer

0.6

Answer

0.4

Answer

0.24

Question 36

A survey found that 40% of students like math, 30% like science, and 20% like both math and science.  What is the probability that a randomly chosen student likes math or science?

Accepted Answer

0.5

Answer

0.9

Answer

0.3

Answer

0.7

Question 37

Two events, A and B, are mutually exclusive if:

Accepted Answer

They cannot occur at the same time.

Answer

They are both equally likely to occur.

Answer

The occurrence of one event increases the probability of the other event occurring.

Answer

The occurrence of one event decreases the probability of the other event occurring.

Question 38

If the probability of event A is 0.3 and the probability of event B is 0.4, what is the probability of both events A and B happening?

Accepted Answer

0.12

Answer

0.4

Answer

0.24

Answer

0.3

Question 39

A bag contains 5 red marbles and 3 blue marbles.  A red marble is drawn and not put back in the bag.  What is the probability of then drawing a blue marble?

Accepted Answer

3/7

Answer

3/8

Answer

5/8

Answer

5/7

Question 40

Events A and B are independent. If the probability of event A is 0.4 and the probability of event B is 0.3, what is the probability of both events A and B happening?

Accepted Answer

0.12

Answer

0.7

Answer

Cannot be determined

Answer

0.58

Question 41

A survey found that 60% of students own a smartphone and 40% own a laptop.  If owning a smartphone and owning a laptop are independent events, what is the probability that a randomly chosen student owns both a smartphone and a laptop?

Accepted Answer

24%

Answer

100%

Answer

60%

Answer

40%

Question 42

The probability of a student passing a math test is 0.8.  If the student passes the math test, the probability of passing the science test is 0.7.  What is the probability of the student passing both tests?

Accepted Answer

0.56

Answer

0.8

Answer

0.14

Answer

0.24

Question 43

Which of the following statements is TRUE about independent events?

Accepted Answer

The occurrence of one event does not affect the probability of the other event occurring.

Answer

The probability of one event is always greater than the other.

Answer

The events cannot occur at the same time.

Question 44

If P(A|B) = P(A), what can you conclude about events A and B?

Accepted Answer

Events A and B are independent.

Answer

Event B is more likely to occur than event A.

Answer

Event A is more likely to occur than event B.

Answer

Events A and B are dependent.

Question 45

In a group of 100 people, 30 like to watch football, 50 like to watch basketball, and 20 like to watch both. What is the probability that a randomly selected person likes to watch football, given that they like to watch basketball?

Accepted Answer

0.4

Answer

0.2

Answer

0.3

Answer

0.5

Question 46

Events A and B are mutually exclusive. If P(A) = 0.2 and P(B) = 0.5, what is P(A or B)?

Accepted Answer

0.7

Answer

Cannot be determined

Answer

0.1

Answer

0.3

Question 47

Two events are independent if and only if:

Accepted Answer

P(A and B) = P(A) * P(B)

Answer

P(A|B) = P(B|A)

Answer

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

Answer

P(A and B) = P(A) + P(B)

Question 48

A box contains red and blue balls.  Drawing a red ball and then drawing a blue ball WITHOUT replacement are examples of:

Accepted Answer

Dependent events

Answer

Independent events

Answer

Equally likely events

Answer

Mutually exclusive events

Question 49

A bag contains 3 red balls, 5 blue balls, and 2 green balls. If a ball is drawn randomly from the bag, what is the probability that it is blue, given that it is not red?

Accepted Answer

5/8

Answer

3/8

Answer

2/8

Answer

1/8

Question 50

A bag contains 6 blue marbles and 4 red marbles. If two marbles are drawn randomly from the bag without replacement, what is the probability that the first marble is blue and the second marble is red?

Accepted Answer

4/15

Answer

8/15

Answer

1/15

Answer

6/15

Question 51

Which of the following is true about independent events?

Accepted Answer

The probability of one event occurring does not affect the probability of the other event occurring

Answer

The probability of both events occurring is always 1

Answer

The probability of one event occurring is always greater than the probability of the other event occurring

Question 52

A company conducted a survey and found that 60% of their employees use a laptop, 40% use a desktop, and 20% use both. If an employee is chosen at random, what is the probability that they use a desktop given that they use a laptop?

Accepted Answer

1/3

Answer

2/3

Answer

1/4

Answer

1/2

Question 53

Which of the following is an example of dependent events?

Accepted Answer

Drawing a card from a deck and then drawing another card without replacing the first card

Answer

Flipping a coin twice and getting heads both times

Answer

Rolling a die and then rolling another die with different numbers on its faces

Question 54

A bag contains 7 red marbles, 5 blue marbles, and 3 green marbles. If two marbles are drawn randomly from the bag with replacement, what is the probability that both marbles are red?

Accepted Answer

49/169

Answer

7/13

Answer

3/13