Probability Quizzes: Test Your Understanding of Chance and Probability

Question 1

A company claims that their product has a failure rate of 5%. If 200 units of the product are sold, what is the expected number of units that will fail?

Accepted Answer

5

Answer

10

Answer

15

Answer

20

Question 2

A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. Two marbles are drawn at random, with replacement. What is the probability of drawing a red marble first and then a blue marble?

Accepted Answer

3 / 10

Answer

1 / 5

Answer

1 / 2

Answer

3 / 5

Question 3

A fair coin is tossed three times. What is the probability of getting at least two heads?

Accepted Answer

3 / 4

Answer

1 / 4

Answer

1 / 2

Answer

1

Question 4

Two events A and B are independent if:

Accepted Answer

P(A ∩ B) = P(A) × P(B)

Answer

P(A ∩ B) = P(A) + P(B)

Answer

P(A | B) = P(A)

Answer

P(B | A) = P(B)

Question 5

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's not red?

Accepted Answer

3/5

Answer

1/5

Answer

1/2

Answer

2/5

Question 6

A fair dice is rolled twice. What's the probability that the sum of the numbers on the top faces is 7?

Accepted Answer

1/12

Answer

1/6

Answer

1/9

Answer

1/18

Question 7

What is the probability density function (PDF) of a continuous uniform distribution defined over the interval (a, b)?

Accepted Answer

f(x) = 1/(b-a)

Answer

f(x) = (x-a)/(b-a)

Answer

f(x) = (b-x)/(b-a)

Answer

f(x) = 1

Question 8

Which of the following is an example of a continuous probability distribution?

Accepted Answer

Normal distribution

Answer

Binomial distribution

Answer

Poisson distribution

Answer

Hypergeometric distribution

Question 9

A coin is tossed 5 times. What is the probability of getting exactly 3 heads?

Accepted Answer

0.3125

Answer

0.25

Answer

0.4375

Answer

0.5

Question 10

Which of the following is the formula for the probability of event A, conditional on event B?

Accepted Answer

P(A) / P(B)

Answer

P(B) / P(A)

Answer

P(A ∩ B)

Answer

P(A) + P(B)

Question 11

What is the expected value of a discrete random variable X with probability mass function P(x)?

Accepted Answer

∑[x * P(x)]

Answer

∫[x * P(x)]

Answer

∑[P(x) / x]

Answer

∫[P(x) / x]

Question 12

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

Accepted Answer

1/6

Answer

1/3

Answer

1/4

Answer

1/5

Question 13

A bag contains 10 balls, numbered 1 to 10. Two balls are drawn without replacement. What is the probability of drawing the number 7 and then the number 5?

Accepted Answer

1/45

Answer

1/10

Answer

1/20

Answer

1/50

Question 14

From a bag containing 5 red balls and 3 blue balls, what is the probability of drawing a blue ball in a single draw?

Accepted Answer

3 / 8

Answer

1 / 2

Answer

1 / 4

Answer

5 / 8

Question 15

A committee of 5 people is to be chosen from a group of 10 women and 8 men. What is the probability that the committee will include 3 women and 2 men?

Accepted Answer

5 / 168

Answer

5 / 84

Answer

10 / 84

Answer

10 / 168

Question 16

A fair coin is tossed four times. What is the probability of getting exactly two heads?

Accepted Answer

3/8

Answer

1/4

Answer

1/8

Answer

1/2

Question 17

A bag contains 5 red balls and 3 blue balls. Two balls are drawn at random without replacement. What is the probability that at least one of the balls drawn is red?

Accepted Answer

13/15

Answer

1/3

Answer

1/2

Answer

2/5

Question 18

A coin is flipped 4 times. What is the probability of getting 2 heads and 2 tails?

Accepted Answer

3/8

Answer

1/2

Answer

1/4

Question 19

A box contains 6 different colored marbles: red, orange, yellow, green, blue, and purple. Three marbles are drawn at random without replacement. What is the probability that the second marble drawn is orange given that the first marble drawn is red?

Accepted Answer

1/5

Answer

1/4

Answer

1/3

Answer

1/6

Question 20

A card is drawn from a standard deck of 52 cards. What is the probability that the card is a spade or a king?

Accepted Answer

1/4

Answer

1/2

Answer

1/3

Answer

1/5

Question 21

A company has 5 managers and 15 non-managers. A committee of 3 people is to be formed, consisting of at least one manager. What is the probability that the committee will have more than one manager?

Accepted Answer

5/8

Answer

1/2

Answer

1/4

Answer

3/8

Question 22

A bag contains 5 red balls, 3 blue balls, and 2 green balls. What is the probability of randomly drawing a red ball from the bag?

Accepted Answer

5/10

Answer

7/10

Answer

3/10

Answer

2/10

Question 23

If a fair coin is tossed twice, what is the probability of getting heads on both tosses?

Accepted Answer

1/4

Answer

1/2

Answer

1/3

Answer

1/8

Question 24

A fair coin is flipped twice. What is the probability of getting at least one head?

Accepted Answer

3/4

Answer

1/4

Answer

1/2

Answer

2/4

Question 25

A bag contains 5 identical balls, numbered 1 to 5. Two balls are drawn randomly without replacement. What is the probability that the sum of the numbers on the drawn balls is even?

Accepted Answer

1/2

Answer

1/3

Answer

1/4

Answer

2/5

Question 26

A fair coin is flipped twice. What is the probability of getting at least one head?

Accepted Answer

3/4

Answer

1/2

Answer

2/3

Answer

1/4

Question 27

A standard six-sided die is rolled. What is the expected value of the number rolled?

Accepted Answer

3.5

Answer

3

Answer

6

Answer

4

Question 28

A bag contains 5 red balls and 3 blue balls. Two balls are drawn at random without replacement. What is the probability that both balls are red?

Accepted Answer

5/14

Answer

5/8

Answer

2/7

Answer

1/2

Question 29

A fair coin is tossed 5 times. What is the probability of getting exactly 3 heads?

Accepted Answer

10/32

Answer

1/2

Answer

5/32

Answer

1/8

Question 30

A survey found that 60% of students like pizza, 70% like burgers, and 40% like both. What is the probability that a randomly chosen student likes pizza given that they like burgers?

Accepted Answer

4/7

Answer

2/3

Answer

6/7

Answer

3/5

Question 31

Two events, A and B, are independent. If P(A) = 0.4 and P(B) = 0.6, what is P(A and B)?

Accepted Answer

0.24

Answer

1

Answer

0.1

Answer

0.7

Question 32

A bag contains 3 red balls, 2 blue balls, and 5 green balls. What is the probability of picking a blue ball at random?

Accepted Answer

2/10

Answer

5/10

Answer

3/10

Answer

1/10

Question 33

A fair coin is tossed three times. What is the probability of getting at least two heads?

Accepted Answer

1/2

Answer

1/4

Answer

1/8

Answer

3/8

Question 34

A box contains 5 red pens and 3 blue pens. Two pens are drawn at random without replacement. What is the probability that both pens are red?

Accepted Answer

5/14

Answer

10/56

Answer

5/8

Question 35

A student has a 70% chance of passing a Maths test and a 60% chance of passing a Physics test. Assuming the tests are independent, what is the probability of the student passing both tests?

Accepted Answer

0.42

Answer

0.13

Answer

0.85

Answer

0.65

Question 36

A die is rolled. What is the probability of getting a number greater than 4 or an even number?

Accepted Answer

2/3

Answer

5/6

Answer

1/2

Answer

1/3

Question 37

A bag contains 4 red balls and 6 blue balls. A ball is drawn at random and replaced. Another ball is then drawn at random. What is the probability that both balls are the same colour?

Accepted Answer

1/2

Answer

2/5

Answer

3/5

Answer

1/5

Question 38

A survey found that 60% of students like Maths, 50% like English, and 30% like both. What is the probability that a randomly selected student likes Maths but not English?

Accepted Answer

0.3

Answer

0.6

Answer

0.2

Answer

0.9

Question 39

The probability of winning a lottery is 1/1000000. If 1000000 tickets are sold, what is the expected number of winners?

Accepted Answer

1

Answer

1000

Answer

10000

Answer

100

Question 40

A fair coin is tossed 10 times. What is the most likely outcome?

Accepted Answer

5 heads and 5 tails

Answer

6 heads and 4 tails

Answer

10 heads

Answer

10 tails

Question 41

A box contains 10 balls, numbered from 1 to 10. A ball is drawn at random. What is the probability that the number on the ball is a prime number?

Accepted Answer

4/10

Answer

3/10

Answer

5/10

Answer

6/10