Probability Quizzes: Test Your Understanding of Chance and Probability

Question 1

A bag has 5 red, 3 blue, and 2 green balls. You draw a ball, replace it, and draw again. What's the chance of drawing red first and blue second?

Accepted Answer

3/20

Answer

1/10

Answer

1/4

Answer

9/10

Question 2

When rolling a fair six-sided dice, what's the chance of getting a 6?

Accepted Answer

1 in 6

Answer

1 in 3

Answer

1 in 4

Answer

1 in 2

Question 3

A school has 300 students. The probability of a student being absent on any given day is 15%. What is the expected number of students absent on a given day?

Accepted Answer

45

Answer

40

Answer

35

Answer

30

Question 4

What is the primary purpose of Bayes' theorem?

Accepted Answer

Calculating the probability of an event based on known probabilities of related events

Answer

Determining the probability of a future event

Answer

Predicting the outcome of a random experiment

Answer

Calculating the expected value of a probability distribution

Question 5

A bag contains 5 black socks, 3 white socks, and 2 grey socks. If 2 socks are drawn randomly without replacing them, what is the probability of drawing two black socks?

Accepted Answer

1/15

Answer

1/5

Answer

1/9

Answer

1/25

Question 6

A fair six-sided die is rolled. What is the probability distribution for the number of dots that appear on the top face?

Accepted Answer

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

Answer

{1: 0.2, 2: 0.2, 3: 0.2, 4: 0.2, 5: 0.2, 6: 0.2}

Answer

{1: 0.5, 2: 0.5}

Answer

{1: 1/3, 2: 1/3, 3: 1/3}

Question 7

A bag contains 4 red balls, 3 blue balls, and 2 green balls. If a ball is drawn at random, what is the probability that it is not blue?

Accepted Answer

5/8

Answer

1/4

Answer

1/2

Answer

3/8

Question 8

A bag contains 5 red marbles and 7 blue marbles. If three marbles are drawn from the bag without replacement, what is the probability that all three marbles are red?

Accepted Answer

5/21

Answer

1/7

Answer

1/2

Answer

5/7

Question 9

Bayes' theorem can be used to calculate the:

Accepted Answer

Probability of an event occurring given that another event has already occurred

Answer

Conditional probability of two independent events

Answer

Probability of a compound event

Answer

Expected value of a random variable

Question 10

A company employs 200 people. The probability that a randomly selected employee is male is 0.6. What is the expected number of male employees in the company?

Accepted Answer

120

Answer

100

Answer

140

Answer

160

Question 11

A survey found that 60% of people own a cat, 40% own a dog, and 20% own both a cat and a dog. What is the probability that a randomly selected person owns a cat or a dog?

Accepted Answer

0.9

Answer

0.6

Answer

0.8

Answer

1.0

Question 12

What is Bayes' theorem primarily used for?

Accepted Answer

To calculate the probability of an event based on conditional probabilities

Answer

To calculate the probability of a conditional event

Answer

To calculate the probability of two independent events

Answer

To calculate the probability of a mutually exclusive event

Question 13

A fair die is rolled twice. What is the probability of getting a sum of 7?

Accepted Answer

1 out of 12

Answer

1 out of 6

Answer

1 out of 18

Answer

1 out of 24

Question 14

A tree diagram shows the possible outcomes of flipping a coin twice. Which branch represents the outcome 'two heads'?

Accepted Answer

HH

Answer

HT

Answer

TH

Answer

TT

Question 15

A fair six-sided die is rolled twice. What is the probability of obtaining an even number on the first roll and an odd number on the second roll?

Accepted Answer

1 in 3

Answer

1 in 6

Answer

1 in 2

Answer

2 in 3

Question 16

The primary purpose of Bayes' theorem is to:

Accepted Answer

Calculate the probability of an event based on updated information.

Answer

Calculate the probability of multiple events occurring.

Answer

Calculate the expected value of a random variable.

Answer

Calculate the variance of a random variable.

Question 17

A bag contains 5 red balls and 3 blue balls. If you draw two balls one after the other without replacing the first ball, what is the probability of drawing a red ball first and then a blue ball?

Accepted Answer

5/12

Answer

3/8

Answer

1/3

Answer

1/2

Question 18

What is the probability of rolling a 6 on a standard six-sided dice?

Accepted Answer

1/6

Answer

1/4

Answer

1/5

Answer

1/7

Question 19

A bag has 5 red marbles and 3 blue marbles. You pick one marble, then another without putting the first one back. What's the probability of picking a red marble followed by a blue marble?

Accepted Answer

15/56

Answer

5/8

Answer

3/8

Answer

5/14

Question 20

A bag has 4 red balls and 6 blue balls. You pick a ball, then put it back. Then you pick another ball. What's the chance you picked a red ball, then a blue ball?

Accepted Answer

3/10

Answer

3/5

Answer

1/2

Answer

2/5

Question 21

A game uses a fair die. You win £5 if you roll a 6, but lose £1 for any other number. On average, how much would you expect to win or lose per game?

Accepted Answer

-£0.17

Answer

£1

Answer

£5

Answer

£0.83

Question 22

A bag has 5 red marbles and 3 blue marbles. If you pick one marble at random, what's the chance of getting a blue marble?

Accepted Answer

3/8

Answer

1/2

Answer

1/3

Answer

5/8

Question 23

A fair coin is flipped three times. What is the probability of getting exactly two heads?

Accepted Answer

3/8

Answer

1/8

Answer

1/2

Answer

1/4

Question 24

A box has 10 light bulbs, with 2 being faulty. If you pick two bulbs without putting the first one back, what's the chance both are faulty?

Accepted Answer

1/45

Answer

2/9

Answer

1/10

Answer

1/50

Question 25

A survey shows 70% of students like chocolate ice cream, 40% like vanilla, and 30% like both. What's the probability a student likes chocolate ice cream if they already like vanilla?

Accepted Answer

3/4

Answer

3/10

Answer

1/2

Answer

7/10

Question 26

A company makes light bulbs with a 1% defect rate. If you pick 100 bulbs randomly, how many are expected to be faulty?

Accepted Answer

1

Answer

10

Answer

0.1

Answer

5

Question 27

A fair die is rolled. If you know the number is even, what's the chance it's greater than 4?

Accepted Answer

1/3

Answer

2/3

Answer

1/2

Answer

1/6

Question 28

A spinner has 5 equal sections, numbered 1 to 5. If you spin it twice, what's the chance the numbers add up to 7?

Accepted Answer

2/25

Answer

1/5

Answer

1/25

Answer

3/25

Question 29

A bag has 3 red balls, 2 blue balls, and 1 green ball. What's the chance of picking a red ball, then a blue ball, without putting the red ball back?

Accepted Answer

1/10

Answer

3/20

Answer

1/5

Question 30

You flip a coin 4 times. What's the probability of getting at least one head?

Accepted Answer

15/16

Answer

1/2

Answer

7/8

Answer

1/16

Question 31

Two events, A and B, are independent. If the chance of event A happening is 0.4 and the chance of event B happening is 0.6, what's the chance of both happening?

Accepted Answer

0.24

Answer

1

Answer

0.5

Answer

0.1