Probability Quizzes for Advanced Diploma in Public Services

Question 1

A survey of 1000 adults found that 60% of them own a smartphone. What is the probability that a randomly selected adult from the survey does not own a smartphone?

Accepted Answer

0.4

Answer

0.5

Answer

0.6

Answer

0.7

Question 2

Bayes' theorem is used to:

Accepted Answer

Calculate the probability of an event based on its prior probability and its likelihood.

Answer

Calculate the probability of an event based on its complement.

Answer

Calculate the probability of an event based on its intersection with another event.

Answer

Calculate the probability of an event based on its union with another event.

Question 3

Which of the following is NOT a characteristic of a probability distribution?

Accepted Answer

The probability of an outcome can be negative.

Answer

The sum of probabilities of all possible outcomes is 1.

Answer

The probability of each outcome is between 0 and 1.

Answer

The mean of the distribution is equal to the expected value.

Question 4

What is the standard deviation of a random variable with a mean of 5 and a variance of 9?

Accepted Answer

3

Answer

2

Answer

6

Answer

9

Question 5

An experiment is conducted 100 times, and an event occurs 45 times. What is the experimental probability of the event?

Accepted Answer

0.45

Answer

0.045

Answer

0.9

Answer

1

Question 6

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

Accepted Answer

1 in 4

Answer

1 in 2

Answer

3 in 4

Answer

1 in 1

Question 7

Which of the following is not a common method for calculating probability?

Accepted Answer

Subjective probability

Answer

Theoretical probability

Answer

Experimental probability

Answer

Conditional probability

Question 8

A bag contains 5 red balls and 3 blue balls. If one ball is drawn at random, what is the probability of drawing a red ball?

Accepted Answer

5/8

Answer

1/2

Answer

2/3

Answer

3/8

Question 9

Bayes' theorem is primarily used for:

Accepted Answer

Calculating posterior probability based on prior probability and likelihood

Answer

Calculating theoretical probability of an event

Answer

Calculating experimental probability from sample data

Answer

Determining the correlation between two events

Question 10

If events A and B are independent and P(A) = 0.6 and P(B) = 0.5, what is the probability of both events occurring?

Accepted Answer

0.3

Answer

0.6

Answer

0.8

Answer

1.1

Question 11

A test has 10 multiple choice questions with four answer options each. If a student randomly guesses on each question, what is the probability of getting all questions correct?

Accepted Answer

0.00001

Answer

0.01

Answer

0.1

Answer

0.001

Question 12

Which of the following statements is NOT true about the axioms of probability?

Accepted Answer

P(A) + P(not A) > 1

Answer

P(A) = 0 if and only if A is an impossible event

Answer

P(A and B) = P(A) + P(B) if A and B are mutually exclusive

Answer

For any event A, 0 ≤ P(A) ≤ 1

Question 13

A game has a 1 in 10 chance of winning. If the game is played 100 times, what is the expected number of losses?

Accepted Answer

90

Answer

5

Answer

15

Answer

20

Question 14

Which of the following is the complement of the event B = rolling a number divisible by 3 on a six-sided die?

Accepted Answer

Rolling a number not divisible by 3

Answer

Rolling an even number

Answer

Rolling a number greater than 4

Question 15

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

Accepted Answer

3/8

Answer

1/4

Answer

1/2

Question 16

A bag contains 5 red balls, 3 blue balls, and 2 green balls. If one ball is chosen at random, what is the probability that it is blue?

Accepted Answer

3/10

Answer

1/5

Answer

1/3

Answer

1/2

Question 17

A die is rolled 100 times. The results are: 1 appears 15 times, 2 appears 18 times, 3 appears 17 times, 4 appears 20 times, 5 appears 16 times, and 6 appears 14 times. What is the experimental probability of rolling a 4?

Accepted Answer

0.2

Answer

0.14

Answer

0.18

Answer

1/6

Question 18

A box contains 10 light bulbs, 3 of which are defective. If two bulbs are chosen at random, without replacement, what is the probability that both are defective?

Accepted Answer

1/15

Answer

3/10

Answer

1/5

Question 19

A survey found that 70% of people in a community own a car, and 40% own both a car and a bicycle. What is the probability that a randomly selected person owns a bicycle, given that they own a car?

Accepted Answer

4/7

Answer

2/5

Answer

4/5

Answer

2/7

Question 20

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 21

A company has 50 employees. 20 are male and 30 are female. If one employee is selected at random, what is the probability of selecting a female employee?

Accepted Answer

3/5

Answer

2/5

Answer

1/3

Answer

1/2

Question 22

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

Accepted Answer

3/10

Answer

1/5

Answer

2/5

Answer

4/7

Question 23

A coin is tossed twice. What is the probability of getting two tails?

Accepted Answer

1/4

Answer

1/3

Answer

1/2

Answer

3/4

Question 24

A die is rolled. What is the probability of getting an even number or a number greater than 3?

Accepted Answer

2/3

Answer

1/6

Answer

1/3

Answer

1/2

Question 25

A card is drawn from a standard deck of 52 cards. What is the probability of drawing a Jack given that it is a black card?

Accepted Answer

2/26

Answer

1/13

Answer

1/4

Answer

1/2

Question 26

A box contains 5 red balls and 3 blue balls. Two balls are drawn at random with replacement. What is the probability that both balls are red?

Accepted Answer

1/4

Answer

5/16

Answer

5/8

Answer

3/10

Question 27

A survey found that 70% of people in a town prefer coffee, and 40% prefer both coffee and tea. What is the probability that a randomly selected person prefers tea only?

Accepted Answer

3/10

Answer

4/5

Answer

2/5

Answer

3/7

Question 28

A fair coin is tossed 10 times. What is the probability of getting exactly 5 heads?

Accepted Answer

252/1024

Answer

1/1024

Answer

1/10

Answer

1/2

Question 29

A company produces light bulbs. 2% of the bulbs are defective. What is the probability that in a sample of 100 bulbs, more than 3 are defective?

Accepted Answer

0.0498

Answer

0.98

Answer

0.02

Answer

0.2

Question 30

A bag contains 4 red balls and 6 blue balls. Two balls are drawn at random without replacement. What is the probability that both balls are of different colors?

Accepted Answer

13/15

Answer

1/2

Answer

2/5

Answer

1/3

Question 31

A security system has three sensors. Each sensor has a 90% chance of detecting an intruder. What is the probability that the system fails to detect an intruder?

Accepted Answer

0.001

Answer

0.271

Answer

0.9

Answer

0.729