Probability and Chance: Master the Fundamentals of Predicting Outcomes

Question 1

From a bag containing 5 red, 3 green, and 2 blue marbles, a marble is drawn at random. What is the probability of drawing a green marble?

Accepted Answer

3/10

Answer

1/5

Answer

1/2

Answer

2/5

Question 2

A survey of 100 students revealed that 60 like math and 50 like science. If 20 students like both math and science, what is the probability that a randomly chosen student likes either math or science?

Accepted Answer

0.8

Answer

0.6

Answer

0.7

Answer

0.9

Question 3

A box contains 4 defective and 6 non-defective light bulbs. If two bulbs are drawn at random without replacement, what is the probability of drawing both defective bulbs?

Accepted Answer

1/15

Answer

1/10

Answer

1/6

Answer

1/5

Question 4

A fair coin is tossed three times. What is the probability of getting a sequence of heads, tails, and heads (H, T, H)?

Accepted Answer

1/8

Answer

1/2

Answer

1/4

Answer

1/16

Question 5

A jar contains 5 red balls and 3 blue balls. If two balls are drawn at random without replacement, what is the probability that both balls are blue?

Accepted Answer

1/12

Answer

1/6

Answer

1/4

Answer

1/3

Question 6

A diagnostic test has a sensitivity of 90% and a specificity of 80%. If 1% of the population has the disease, what is the probability that a person who tests positive actually has the disease?

Accepted Answer

0.11

Answer

0.01

Answer

0.09

Answer

0.12

Question 7

A coin is flipped three times. What is the probability of getting at least one head?

Accepted Answer

3 out of 4

Answer

1 out of 8

Answer

1 out of 4

Answer

1 out of 2

Question 8

A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. If two marbles are drawn randomly without replacement, what is the probability of drawing a red marble and then a blue marble?

Accepted Answer

3/10

Answer

1/10

Answer

1/5

Answer

1/3

Question 9

Which of the following is NOT a characteristic of probability?

Accepted Answer

It is subjective

Answer

It is a number between 0 and 1 inclusive

Answer

It is additive

Answer

It is always positive

Question 10

A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. What is the probability of drawing a blue or green marble?

Accepted Answer

2/5

Answer

1/2

Answer

1/5

Answer

1/3

Question 11

Which of the following is NOT a type of discrete probability distribution?

Accepted Answer

Normal distribution

Answer

Binomial distribution

Answer

Poisson distribution

Answer

Exponential distribution

Question 12

What are mutually exclusive events? Explain their significance with real-life examples.

Accepted Answer

Events that cannot happen at the same time

Answer

Events that do not affect each other

Answer

Events with a combined probability of 1

Answer

Events that have no practical importance

Question 13

A school has 200 students. 120 students are in the 11th grade. What is the probability that a randomly selected student is in the 11th grade?

Accepted Answer

0.4

Answer

0.5

Answer

0.6

Answer

0.7

Question 14

The probability of an event happening is 0.4. What is the probability of the event not happening?

Accepted Answer

0.6

Answer

0.4

Answer

0.8

Answer

0.2

Question 15

A bag contains 5 coins. Two coins are drawn at random. What is the probability that both coins are heads?

Accepted Answer

1/16

Answer

1/4

Answer

1/8

Answer

1/32

Question 16

From a bag containing 5 red balls, 3 blue balls, and 2 green balls, what is the probability of drawing a red ball, expressed as a fraction?

Accepted Answer

1/5

Answer

2/5

Answer

3/5

Answer

4/5

Question 17

A test has 10 multiple-choice questions, each with 4 possible answers. What is the probability of randomly guessing the correct answer to all 10 questions?

Accepted Answer

1/1024

Answer

1/4

Answer

1/10

Answer

0

Question 18

Bayes' theorem is used to calculate the probability of an event based primarily on:

Accepted Answer

Conditional probabilities

Answer

Prior knowledge

Answer

Independent events

Answer

Sample space size

Question 19

Which of the following is NOT a fundamental property of probability distributions?

Accepted Answer

Probabilities can be greater than 1.

Answer

The sum of probabilities equals 1.

Answer

Probabilities are always positive.

Answer

Events are mutually exclusive.

Question 20

Which of the following is NOT a possible disadvantage of using Bayes' theorem?

Accepted Answer

It is universally applicable to any probability problem.

Answer

It may require a large sample size.

Answer

It can be computationally complex.

Answer

It assumes independence of events.

Question 21

What is conditional probability?

Accepted Answer

The probability of an event happening given that another event has already happened

Answer

The probability of two events happening at the same time

Answer

The probability of an event happening twice in a row

Answer

The probability of an event not happening

Question 22

Which of the following is NOT an assumption of Bayes' theorem?

Accepted Answer

The events being considered are independent

Answer

The prior probabilities of the events are known

Answer

The events are exhaustive

Answer

The events are mutually exclusive

Question 23

Which of the following is a continuous probability distribution?

Accepted Answer

Normal distribution

Answer

Bernoulli distribution

Answer

Poisson distribution

Answer

Binomial distribution

Question 24

What is the standard deviation of a normal distribution with mean 10 and variance 4?

Accepted Answer

2

Answer

1

Answer

3

Answer

4

Question 25

Two fair dice are rolled. What is the probability of obtaining a sum greater than 9?

Accepted Answer

5 / 12

Answer

1 / 4

Answer

1 / 6

Answer

1 / 12

Question 26

Given that the probability of event A is 0.4 and the probability of event B is 0.6, what is the probability of either A or B occurring (i.e., P(A ∪ B))?

Accepted Answer

0.8

Answer

0.2

Answer

0.24

Answer

1

Question 27

Two cards are drawn from a standard deck of 52 cards without replacement. What is the probability that the first card is a heart and the second card is a spade?

Accepted Answer

1 / 104

Answer

1 / 26

Answer

1 / 52

Answer

1 / 208

Question 28

A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. If a marble is drawn randomly, what is the probability of selecting a red marble?

Accepted Answer

1/5

Answer

1/2

Answer

1/3

Answer

1/10

Question 29

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

Accepted Answer

The distribution can have both positive and negative values.

Answer

The sum of the probabilities of all outcomes equals 1.

Answer

The probability of any one outcome is between 0 and 1.

Answer

The distribution can be used to predict future events.

Question 30

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

Accepted Answer

Binomial distribution

Answer

Normal distribution

Answer

Exponential distribution

Answer

Uniform distribution

Question 31

A coin is flipped twice. What is the probability of obtaining heads on the first flip and tails on the second flip?

Accepted Answer

1/8

Answer

1/4

Answer

1/2

Answer

1/16

Question 32

A restaurant offers a 15% discount for customers who order online. If 60% of customers order online, what is the probability that a randomly selected customer will receive the discount?

Accepted Answer

0.21

Answer

0.15

Answer

0.60

Answer

0.84

Question 33

A bag contains 5 red balls, 3 blue balls, and 2 yellow balls. If a ball is drawn at random, what is the probability of drawing a red ball?

Accepted Answer

1/5

Answer

1/10

Answer

3/10

Answer

1/2

Question 34

A coin is tossed twice. What is the probability of getting 'heads' on both tosses?

Accepted Answer

1/8

Answer

1/4

Answer

1/2

Answer

1/16

Question 35

When two dice are rolled, what is the probability of getting a sum of 7?

Accepted Answer

1 / 12

Answer

1 / 6

Answer

1 / 18

Answer

1 / 24

Question 36

A card is drawn from a standard deck of 52 cards. What is the probability of drawing a face card (jack, queen, or king)?

Accepted Answer

3 / 13

Answer

1 / 4

Answer

1 / 13

Answer

1 / 2

Question 37

A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. What is the probability of randomly selecting a blue marble?

Accepted Answer

3/10

Answer

2/5

Answer

5/10

Answer

1/5

Question 38

Two fair dice are rolled. What is the probability of getting a sum of 7 or 11?

Accepted Answer

2/9

Answer

1/3

Answer

1/9

Answer

1/6

Question 39

Events A and B are mutually exclusive. If P(A) = 0.4 and P(B) = 0.3, what is P(A or B)?

Accepted Answer

0.7

Answer

0.12

Answer

Cannot be determined

Answer

0.1

Question 40

A company produces light bulbs, and 3% of the bulbs are defective. What is the probability that in a sample of 5 bulbs, at least one is defective?

Accepted Answer

0.14

Answer

0.03

Answer

0.09

Question 41

A random variable X has the following probability distribution:

P(X=0) = 0.3, P(X=1) = 0.4, P(X=2) = 0.3.

What is the expected value of X?

Accepted Answer

1.0

Answer

1.5

Answer

2.0

Answer

0.5

Question 42

In a medical test, 99% of people with a certain disease test positive, and 1% of people without the disease also test positive (false positive). If 0.5% of the population has the disease, what is the probability that a person who tests positive actually has the disease?

Accepted Answer

0.980

Answer

0.01

Answer

0.005

Answer

0.5

Question 43

Which of the following is NOT an assumption of a binomial experiment?

Accepted Answer

Trials are dependent.

Answer

There are only two possible outcomes.

Answer

Trials are independent.

Question 44

The probability that a basketball player makes a free throw is 0.7. What is the probability that the player makes exactly 6 out of 10 free throws?

Accepted Answer

0.199

Answer

0.077

Answer

0.7

Answer

0.49

Question 45

A bag contains 3 red marbles, 2 blue marbles, and 5 green marbles. If two marbles are drawn without replacement, what is the probability of drawing a red marble and then a blue marble?

Accepted Answer

6/50

Answer

1/2

Answer

3/25

Answer

1/5

Question 46

A fair coin is tossed four times. What is the probability of getting at least one tail?

Accepted Answer

15/16

Answer

1/2

Answer

1/16

Answer

1/4

Question 47

A standard deck of cards has 52 cards. What is the probability of drawing a king or a queen?

Accepted Answer

2/13

Answer

1/52

Answer

1/26

Answer

1/13

Question 48

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

0.1

Answer

0.7

Answer

1

Question 49

A company produces light bulbs, with 90% of them working properly. A sample of 10 bulbs is selected. What is the probability that at least one bulb is defective?

Accepted Answer

0.6513

Answer

0.3487

Answer

0.9

Answer

0.09

Question 50

A student has a 70% chance of passing a math test and a 60% chance of passing a history test. Assuming the two tests are independent, what is the probability that the student will pass both tests?

Accepted Answer

0.42

Answer

0.65

Answer

1.3

Answer

0.13