Conditional Probability: Interactive Quizzes and Practice Questions

Question 1

Which of the following is NOT a way to represent conditional probability?

Accepted Answer

Venn diagram

Answer

Tree diagram

Answer

Fraction

Answer

Percentage

Question 2

What is the sample space for rolling two dice?

Accepted Answer

{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

Answer

{1, 2, 3, 4, 5, 6}

Answer

{2, 4, 6, 8, 10, 12}

Answer

{3, 6, 9, 12}

Question 3

Which factor does NOT influence conditional probability?

Accepted Answer

The number of trials

Answer

The probability of the initial event

Answer

The outcomes of previous events

Answer

The size of the sample space

Question 4

A bag contains 5 red marbles and 3 blue marbles. You draw a marble and keep it. What is the probability of drawing a blue marble if you draw another marble?

Accepted Answer

3/8

Answer

1/8

Answer

1/2

Answer

5/8

Question 5

A fair coin is tossed twice. What is the probability that the coin lands on heads exactly once?

Accepted Answer

1/4

Answer

1/2

Answer

3/4

Answer

1/8

Question 6

A coin is flipped three times. What is the probability of getting tails on the first flip, heads on the second flip, and tails on the third flip?

Accepted Answer

0.125

Answer

0.25

Answer

0.5

Answer

0.75

Question 7

When rolling a standard six-sided die, what is the chance of landing on an even number?

Accepted Answer

1/2

Answer

1/3

Answer

1/4

Answer

1/6

Question 8

A bag has 5 red marbles and 7 blue marbles. If you pick one marble at random, what is the chance of picking a blue marble?

Accepted Answer

7/12

Answer

5/12

Answer

1/2

Answer

1/4

Question 9

A survey found that 60% of students like math and 40% like science. If 25% of students like both math and science, what is the chance that a student likes science given that they like math?

Accepted Answer

3/5

Answer

1/2

Answer

1/3

Answer

2/5

Question 10

From a box with 3 red, 2 blue, and 5 yellow marbles, two marbles are drawn without replacement. What is the probability of drawing a blue marble first and a yellow marble second?

Accepted Answer

1/10

Answer

1/5

Answer

1/15

Answer

1/20

Question 11

Which of the following is the definition of conditional probability?

Accepted Answer

The probability of an event occurring given that another event has occurred.

Answer

The probability of an event occurring before another event.

Answer

The probability of an event occurring after another event.

Answer

The probability of an event occurring independent of any other event.

Question 12

What is the probability of an event occurring when another event has already happened?

Accepted Answer

Conditional probability

Answer

Independent probability

Answer

Simultaneous probability

Answer

Exclusive probability

Question 13

Which of these represents the conditional probability of event A happening after event B has already happened?

Accepted Answer

P(A|B)

Answer

P(B)

Answer

P(A)

Answer

P(B|A)

Question 14

A bag contains 3 red marbles, 4 blue marbles, and 5 yellow marbles. If you draw a marble at random and replace it, what is the probability of drawing a blue marble the second time?

Accepted Answer

4/12

Answer

3/12

Answer

5/12

Answer

1/3

Question 15

A survey revealed that 60% of students in a school like math, and 20% of all students are in the 6th grade. What is the probability that a randomly selected 6th grader likes math?

Accepted Answer

0.12

Answer

0.3

Answer

0.6

Answer

0.2

Question 16

A box contains 2 green balls and 3 blue balls. Two balls are drawn from the box without replacement. What is the probability that the first ball drawn is green and the second ball is blue?

Accepted Answer

6/25

Answer

1/5

Answer

2/15

Answer

1/2

Question 17

A bag contains black and white balls. If the probability of drawing a black ball is 1/3, what is the probability of drawing a white ball?

Accepted Answer

2/3

Answer

1/3

Answer

1/2

Answer

1

Question 18

In a bag with 3 blue marbles and 5 red marbles, if a marble is chosen randomly, what is the chance of it being blue?

Accepted Answer

1/3

Answer

1/2

Answer

1/4

Answer

1/5

Question 19

What is the probability of flipping a fair coin twice and getting heads on the first flip and tails on the second flip?

Accepted Answer

1/4

Answer

1/2

Answer

3/4

Answer

1

Question 20

You flip a fair coin twice. What is the chance of getting heads on the first flip and tails on the second flip?

Accepted Answer

1/4

Answer

1/2

Answer

1

Answer

2/3

Question 21

What is the correct definition of conditional probability?

Accepted Answer

The probability of a specific event occurring, assuming that another event has already taken place

Answer

The probability of an event happening before another event

Answer

The probability of an event happening after another event

Answer

The probability of two events happening independently

Question 22

A bag contains 4 red marbles, 3 blue marbles, and 2 green marbles. If you draw a marble and it is red, what is the probability of drawing a blue marble as the next draw?

Accepted Answer

3/8

Answer

1/4

Answer

1/2

Answer

3/4

Question 23

You flip a fair coin. What is the probability of getting heads this time, given that the previous flip was tails?

Accepted Answer

50%

Answer

0%

Answer

100%

Answer

Cannot be determined

Question 24

Which of these is an example of conditional probability?

Accepted Answer

The chance of getting sick if you have been exposed to a virus

Answer

The chance of winning a lottery

Answer

The chance of a coin landing on heads

Answer

The chance of the sun rising tomorrow

Question 25

How is conditional probability different from independent probability?

Accepted Answer

Conditional probability depends on the outcome of a previous event, while independent probability does not.

Answer

Independent probability depends on the outcome of a previous event, while conditional probability does not.

Answer

They are the same thing.

Answer

Conditional probability is more likely to happen than independent probability.

Question 26

What is the complement of event "A"?

Accepted Answer

The event that takes place if A does not

Answer

The event that occurs if A happens

Answer

The event that takes place alongside A

Answer

The event that is distinct and non-overlapping with A

Question 27

Two events are mutually exclusive when:

Accepted Answer

They cannot happen at the same time

Answer

They consistently happen together

Answer

One must happen before the other

Answer

They happen in a specific sequence

Question 28

What is the likelihood of an event that is certain to occur?

Accepted Answer

1

Answer

0

Answer

0.5

Answer

Cannot be determined

Question 29

What is the probability of an event that cannot happen?

Accepted Answer

0

Answer

1

Answer

0.5

Answer

Cannot be determined

Question 30

A deck of cards contains 13 hearts. If you draw a heart, what is the probability of drawing a red card next?

Accepted Answer

1/4

Answer

1/13

Answer

1/52

Answer

0

Question 31

A biased coin has a probability of 0.6 of landing on heads. If the coin is tossed twice, what is the probability of getting heads on both tosses?

Accepted Answer

0.36

Answer

0.48

Answer

0.60

Answer

0.72

Question 32

A box contains 5 green balls and 3 red balls. Two balls are drawn randomly, without replacement. What is the probability that the second ball drawn is red, given that the first ball drawn was green?

Accepted Answer

3/8

Answer

1/8

Answer

1/4

Answer

1/2

Question 33

A study found that 60% of students who study for a test pass the test. If a student studies for a test, what is the probability that they will pass?

Accepted Answer

0.6

Answer

0.4

Answer

0.8

Answer

1.0

Question 34

A class of 25 students has 10 boys and 15 girls. The teacher randomly selects three students to represent the class at a school event. What is the probability that all three students are boys?

Accepted Answer

0.06

Answer

0.12

Answer

0.18

Answer

0.24

Question 35

A spinner has 6 equal-sized sections, numbered 1 to 6. The spinner is spun twice. What is the probability that the first spin lands on an even number and the second spin lands on a number less than 4?

Accepted Answer

1/12

Answer

1/6

Answer

1/3

Answer

1/4

Question 36

A deck of cards contains 52 cards. What is the probability of drawing a face card (jack, queen, or king) and then drawing a heart?

Accepted Answer

1/26

Answer

1/13

Answer

1/52

Answer

1/4

Question 37

A bag contains 4 red marbles, 3 blue marbles, and 2 green marbles. If two marbles are drawn without replacement, what is the probability that both marbles are blue?

Accepted Answer

1/12

Answer

1/6

Answer

1/4

Answer

1/3

Question 38

A deck of cards contains 52 cards. What is the probability of drawing an ace and then drawing a spade?

Accepted Answer

1/26

Answer

1/13

Answer

1/52

Answer

1/4

Question 39

A bag contains 6 red marbles, 4 blue marbles, and 3 green marbles. If two marbles are drawn with replacement, what is the probability that both marbles are green?

Accepted Answer

1/36

Answer

1/6

Answer

1/12

Answer

1/18

Question 40

You flip a coin twice. If the first flip is heads, what's the chance of getting tails on the second flip?

Accepted Answer

1/2

Answer

0

Answer

1

Answer

1/4

Question 41

A bag has 2 red balls, 3 blue balls, and 5 green balls. If you pick a ball without looking, what's the chance it's red if you know it's not green?

Accepted Answer

2/5

Answer

1/5

Answer

1/2

Answer

2/8

Question 42

You roll a die twice.  If the first roll is a 3, what's the chance of rolling a 6 on the second roll?

Accepted Answer

1/6

Answer

1/2

Answer

1/12

Answer

1/36

Question 43

A bag has 5 red marbles, 3 blue marbles, and 2 green marbles. You pick a marble, put it back, and then pick another.  What's the chance you pick a blue marble on your second try if you picked a red marble the first time?

Accepted Answer

3/10

Answer

1/3

Answer

2/5

Answer

1/2

Question 44

Out of 100 kids, 60 like math, 40 like science, and 20 like both.  If a kid likes math, what's the chance they also like science?

Accepted Answer

1/3

Answer

1/2

Answer

1/4

Answer

2/5

Question 45

A box has 6 black balls and 4 white balls. You pick one ball, don't put it back, and then pick another. What's the chance you'll pick two white balls in a row?

Accepted Answer

2/15

Answer

1/5

Answer

1/3

Answer

1/6

Question 46

A bag has 3 red marbles, 4 blue marbles, and 5 green marbles. You pick one marble, keep it, and then pick another. What's the chance you'll get two red marbles in a row?

Accepted Answer

3/35

Answer

3/10

Answer

1/5

Answer

1/2

Question 47

A spinner has 4 equal sections labeled A, B, C, and D.  You spin it once and get 'A'.  What's the chance you'll spin 'B' on your next spin?

Accepted Answer

1/4

Answer

1/8

Answer

1

Answer

1/2

Question 48

Out of 100 kids, 60 like pizza, 40 like burgers, and 20 like both.  If a kid likes pizza, what's the chance they also like burgers?

Accepted Answer

1/3

Answer

1/2

Answer

2/5

Question 49

A bag has 5 red marbles, 3 blue marbles, and 2 green marbles. You pick a marble, put it back, and then pick another.  What's the chance you pick a green marble on your second try if you picked a blue marble the first time?

Accepted Answer

2/10

Answer

2/5

Answer

1/2

Answer

1/3

Question 50

Out of 100 kids, 60 like math, 40 like science, and 20 like both.  If a kid likes science, what's the chance they also like math?

Accepted Answer

1/2

Answer

1/3

Answer

1/4

Answer

2/5

Question 51

A box has 6 black balls and 4 white balls. You pick one ball, don't put it back, and then pick another. What's the chance you'll pick a black ball first and then a white ball?

Accepted Answer

4/15

Answer

1/3

Answer

1/6

Answer

1/5

Question 52

A bag has 3 red marbles, 4 blue marbles, and 5 green marbles. You pick one marble, keep it, and then pick another. What's the chance you'll get two green marbles in a row?

Accepted Answer

5/35

Answer

3/10

Answer

1/5

Answer

1/2