Question 1

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

Accepted Answer

Correct Option: B. Solution: The total number of balls is $3 + 2 + 4 = 9$. The number of non-blue balls is $3 + 2 = 5$. Therefore, the probability of drawing a non-blue ball is $\frac{5}{9}$.

Question 2

A deck of cards contains 52 cards. If one card is drawn at random, what is the probability that it is not an ace?

Accepted Answer

Correct Option: C. Solution: There are 4 aces in a deck of 52 cards, so the probability of drawing an ace is $\frac{4}{52} = 0.0769$. Therefore, the probability of not drawing an ace is $1 - 0.0769 = 0.9231$.

Question 3

What is the probability of drawing a card that is not an ace from a well-shuffled deck of 52 cards?

Accepted Answer

Correct Option: B. Solution: There are 4 aces in a deck of 52 cards. The probability of drawing an ace is $4/52 = 1/13$. Therefore, the probability of not drawing an ace is $1 - 1/13 = 12/13$.

Question 4

In a theoretical probability scenario, a fair die is rolled once. What is the probability of rolling a number greater than 4?

Accepted Answer

Correct Option: B. Solution: The possible outcomes when rolling a fair die are 1, 2, 3, 4, 5, and 6. The numbers greater than 4 are 5 and 6. Thus, the probability is $ \frac{2}{6} = \frac{1}{3} $.

Question 5

A fair die is thrown once. What is the probability of getting an elementary event where the outcome is a number greater than 4?

Accepted Answer

Correct Option: A. Solution: The possible outcomes when a die is thrown are 1, 2, 3, 4, 5, and 6. The elementary events where the outcome is greater than 4 are 5 and 6. Therefore, the probability is $\frac{2}{6} = \frac{1}{3}$.

Question 6

In a deck of 52 cards, what is the probability of drawing a card that is not an ace?

Accepted Answer

Correct Option: D. Solution: There are 4 aces in a deck of 52 cards. The probability of drawing an ace is $\frac{4}{52} = \frac{1}{13}$. Therefore, the probability of not drawing an ace is $1 - \frac{1}{13} = \frac{12}{13}$.

Question 7

In a deck of 52 cards, what is the probability of drawing a spade?

Accepted Answer

Correct Option: A. Solution: There are 13 spades in a deck of 52 cards. The probability of drawing a spade is $\frac{13}{52} = \frac{1}{4}$.

Question 8

A bag contains 4 red balls and 1 blue ball. If a ball is drawn at random, what is the probability that the ball drawn is red?

Accepted Answer

Correct Option: D. Solution: There are 4 red balls and 1 blue ball, making a total of 5 balls. The probability of drawing a red ball is the number of red balls divided by the total number of balls, i.e., $\frac{4}{5}$.

Question 9

In a game, a die is thrown once. What is the probability of getting a number greater than 6?

Accepted Answer

Correct Option: A. Solution: A standard die has numbers from 1 to 6. There is no face with a number greater than 6, making the probability of rolling such a number impossible, hence 0.

Question 10

If a die is thrown once, what is the probability of getting a number greater than 4?

Accepted Answer

Correct Option: B. Solution: The numbers greater than 4 on a die are 5 and 6. There are 2 favorable outcomes out of 6 possible outcomes, so the probability is $\frac{2}{6} = \frac{1}{3}$.

Question 11

In a standard deck of 52 playing cards, what is the probability of drawing an elementary event that is a face card?

Accepted Answer

Correct Option: A. Solution: There are 12 face cards (3 face cards per suit) in a deck of 52 cards. The probability of drawing a face card is $\frac{12}{52} = \frac{3}{13}$.

Question 12

What is the theoretical probability of getting a head when a fair coin is tossed once?

Accepted Answer

Correct Option: A. Solution: In a fair coin toss, there are two equally likely outcomes: head and tail. The probability of getting a head is $\frac{1}{2}$.

Question 13

Suppose a fair die is rolled once. What is the probability of getting a number greater than 5?

Accepted Answer

Correct Option: A. Solution: The possible outcomes when a die is rolled are 1, 2, 3, 4, 5, and 6. The number of outcomes greater than 5 is 1 (only 6). Therefore, the probability is $\frac{1}{6}$.

Question 14

If two dice are thrown simultaneously, what is the probability that the sum of the numbers is 8?

Accepted Answer

Correct Option: A. Solution: The outcomes that give a sum of 8 are (2,6), (3,5), (4,4), (5,3), and (6,2). Thus, the probability is $\frac{5}{36}$.

Question 15

A bag contains 3 red balls and 5 black balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is neither red nor black?

Accepted Answer

Correct Option: B. Solution: Since the bag contains only red and black balls, there is no possibility of drawing a ball that is neither red nor black. Therefore, the probability of drawing such a ball is 0.

Question 16

A bag contains 3 red balls and 5 black balls. What is the probability of drawing a red ball?

Accepted Answer

Correct Option: A. Solution: The probability of drawing a red ball is $\frac{3}{3+5} = \frac{3}{8}$.

Question 17

A bag contains 3 red balls, 5 blue balls, and 2 green balls. If a ball is drawn at random, what is the empirical probability that the ball drawn is red, given that in 10 previous draws, 4 red balls were drawn?

Accepted Answer

Correct Option: B. Solution: The empirical probability is calculated as the number of successful outcomes (red balls drawn) divided by the total number of trials. Therefore, the empirical probability is $ \frac{4}{10} = 0.4 $.

Question 18

A standard deck of 52 cards is shuffled and one card is drawn at random. What is the probability that the card drawn is a face card?

Accepted Answer

Correct Option: A. Solution: There are 12 face cards in a deck of 52 cards (3 face cards in each of the 4 suits). Therefore, the probability is $\frac{12}{52} = \frac{3}{13}$.

Question 19

What is the probability of drawing a red face card from a well-shuffled deck of 52 cards?

Accepted Answer

Correct Option: A. Solution: There are 6 red face cards (3 hearts and 3 diamonds) in a deck of 52 cards. The probability is $\frac{6}{52} = \frac{3}{26}$.

Question 20

Which of the following statements is true regarding the probability of events?

Accepted Answer

Correct Option: C. Solution: The probability of a sure event is 1, while the probability of an impossible event is 0.

Question 21

What is the probability of drawing a red ball from a bag containing 4 red balls and 1 blue ball?

Accepted Answer

Correct Option: D. Solution: There are 4 red balls and 1 blue ball, making a total of 5 balls. The probability of drawing a red ball is the number of red balls divided by the total number of balls, which is $\frac{4}{5}$.

Question 22

In a game, a fair coin is tossed three times. What is the probability of getting exactly two heads?

Accepted Answer

Correct Option: B. Solution: The possible outcomes are HHT, HTH, THH. There are 3 favorable outcomes out of 8 possible outcomes (HHH, HHT, HTH, THH, TTH, THT, HTT, TTT). Thus, the probability is $\frac{3}{8}$.

Question 23

In a game of chance, a spinner is divided into 8 equal sections numbered 1 to 8. What is the probability that it will land on an odd number?

Accepted Answer

Correct Option: A. Solution: The odd numbers on the spinner are 1, 3, 5, and 7. There are 4 odd numbers out of 8 total numbers, so the probability is $\frac{4}{8} = \frac{1}{2}$.

Question 24

A spinner is divided into 8 equal sections numbered 1 to 8. If the spinner is spun once, what is the probability of landing on a number greater than 5?

Accepted Answer

Correct Option: A. Solution: The numbers greater than 5 are 6, 7, and 8. There are 3 favorable outcomes out of 8 possible outcomes. Thus, the probability is $\frac{3}{8}$.

Question 25

If the probability of an event $E$ is 0.3, what is the probability of the complementary event $\overline{E}$?

Accepted Answer

Correct Option: B. Solution: The probability of the complementary event $\overline{E}$ is given by $P(\overline{E}) = 1 - P(E) = 1 - 0.3 = 0.7$.

Question 26

A bag contains 4 red balls and 1 blue ball. If one ball is drawn at random, what is the probability that it is not blue?

Accepted Answer

Correct Option: C. Solution: The probability of drawing a blue ball is $P(	ext{blue}) = \frac{1}{5}$. Therefore, the probability of not drawing a blue ball is $P(	ext{not blue}) = 1 - \frac{1}{5} = \frac{4}{5} = 0.8$.

Question 27

A bag contains 3 blue, 2 white, and 4 red marbles. What is the probability of drawing a white marble?

Accepted Answer

Correct Option: B. Solution: There are 2 white marbles and a total of 9 marbles. The probability of drawing a white marble is $\frac{2}{9}$.

Question 28

When two dice are thrown simultaneously, what is the probability of getting a sum of 8?

Accepted Answer

Correct Option: A. Solution: The possible outcomes for a sum of 8 are (2,6), (3,5), (4,4), (5,3), and (6,2). There are 5 favorable outcomes out of 36 possible outcomes when two dice are thrown. Thus, the probability is $\frac{5}{36}$.

Question 29

A die is thrown once. What is the probability of getting a prime number?

Accepted Answer

Correct Option: B. Solution: The prime numbers on a die are 2, 3, and 5. There are 3 prime numbers out of 6 possible outcomes, so the probability is $\frac{3}{6} = \frac{1}{2}$.

Question 30

Two dice are thrown simultaneously. What is the probability that the sum of the numbers on the top faces is 9?

Accepted Answer

Correct Option: B. Solution: The possible outcomes for a sum of 9 are (3,6), (4,5), (5,4), (6,3). There are 4 favorable outcomes out of 36 possible outcomes. Thus, the probability is $\frac{4}{36} = \frac{1}{9}$.

Question 31

In a deck of 52 playing cards, what is the probability of drawing a card that is neither a king nor a queen?

Accepted Answer

Correct Option: A. Solution: There are 4 kings and 4 queens in a deck, totaling 8 cards. Therefore, the number of cards that are neither kings nor queens is $52 - 8 = 44$. Thus, the probability is $\frac{44}{52}$.

Question 32

In a single throw of a die, what is the probability of getting a number less than or equal to 4?

Accepted Answer

Correct Option: D. Solution: The numbers less than or equal to 4 are 1, 2, 3, and 4. Therefore, the probability is $\frac{4}{6} = \frac{2}{3}$.

Question 33

A box contains 5 red marbles, 8 white marbles, and 4 green marbles. If one marble is drawn at random, what is the probability that it is either red or green?

Accepted Answer

Correct Option: A. Solution: The total number of marbles is $5 + 8 + 4 = 17$. The number of red or green marbles is $5 + 4 = 9$. Therefore, the probability is $\frac{9}{17}$.

Question 34

A bag contains 4 red balls and 1 blue ball. If one ball is drawn at random, what is the probability of drawing an elementary event that is a blue ball?

Accepted Answer

Correct Option: A. Solution: There is only 1 blue ball in a total of 5 balls. Thus, the probability of drawing a blue ball is $\frac{1}{5}$.

Question 35

What is the probability of drawing a king of red color from a well-shuffled deck of 52 cards?

Accepted Answer

Correct Option: A. Solution: There are 2 red kings in a deck of 52 cards. Thus, the probability is $\frac{2}{52} = \frac{1}{26}$.

Question 36

In a probability experiment, a spinner is divided into 8 equal sections numbered from 1 to 8. What is the probability that the spinner will land on a number that is a multiple of 3?

Accepted Answer

Correct Option: A. Solution: The numbers that are multiples of 3 are 3 and 6. Therefore, there are 2 favorable outcomes out of 8. Thus, the probability is $\frac{2}{8} = \frac{1}{4}$.

Question 37

A carton contains 100 shirts: 88 are good, 8 have minor defects, and 4 have major defects. What is the probability that a shirt drawn at random is acceptable to Sujatha, who rejects only those with major defects?

Accepted Answer

Correct Option: C. Solution: Sujatha accepts shirts with minor or no defects. Thus, she accepts 88 + 8 = 96 shirts. The probability is $\frac{96}{100} = 0.96$.

Question 38

In a class of 40 students, 25 are girls. If a student is selected at random, what is the probability that the student is not a girl?

Accepted Answer

Correct Option: A. Solution: The probability of selecting a girl is $\frac{25}{40} = 0.625$. Therefore, the probability of not selecting a girl is $1 - 0.625 = 0.375$.

Question 39

Which of the following statements is true about elementary events?

Accepted Answer

Correct Option: B. Solution: An elementary event is an event with only one outcome, and the sum of the probabilities of all elementary events of an experiment is 1.

Question 40

If a die is thrown once, the probability of getting a number greater than 4 is $\frac{1}{3}$.

Accepted Answer

Answer: True. Solution: The possible outcomes greater than 4 are 5 and 6. Thus, the probability is $\frac{2}{6} = \frac{1}{3}$.

Question 41

Empirical probability is based on assumptions and predictions.

Accepted Answer

Answer: False. Solution: Empirical probability is based on actual outcomes of experiments, not on assumptions and predictions.

Question 42

In a single throw of a die, the probability of getting a number less than 7 is 1.

Accepted Answer

Answer: True. Solution: All numbers on a die (1, 2, 3, 4, 5, 6) are less than 7, so the probability is $\frac{6}{6} = 1$.

Question 43

An event with multiple outcomes can be considered an elementary event.

Accepted Answer

Answer: False. Solution: An event with only one outcome is called an elementary event.

Question 44

The probability of getting a sum of 13 when two dice are thrown is 0.

Accepted Answer

Answer: True. Solution: The maximum sum possible when two dice are thrown is 12. Therefore, getting a sum of 13 is impossible, and the probability is 0.

Question 45

The theoretical probability of an event is always calculated assuming equally likely outcomes.

Accepted Answer

Answer: True. Solution: The theoretical probability, also known as classical probability, is defined under the assumption that all outcomes of the experiment are equally likely.

Question 46

The probability of an event and its complement always sum to 1.

Accepted Answer

Answer: True. Solution: For any event $E$, the probability of $E$ and the probability of its complement $E'$ sum to 1, i.e., $P(E) + P(E') = 1$.

Question 47

If the probability of an event $E$ is 0.3, then the probability of its complement is 0.7.

Accepted Answer

Answer: True. Solution: Since $P(E) + P(\overline{E}) = 1$, if $P(E) = 0.3$, then $P(\overline{E}) = 1 - 0.3 = 0.7$.

Question 48

In a fair die throw, the probability of getting a number greater than 4 is 1/3.

Accepted Answer

Answer: True. Solution: When a die is thrown, the numbers greater than 4 are 5 and 6. Thus, there are 2 favorable outcomes out of 6 possible outcomes, giving a probability of 2/6 = 1/3.

Question 49

For any event $E$, the probability of $E$ plus the probability of the complement of $E$ is always 1.

Accepted Answer

Answer: True. Solution: The probability of an event $E$ and its complement $\overline{E}$ must sum to 1, as they encompass all possible outcomes of the event.

Question 50

An elementary event is an event that can have multiple outcomes.

Accepted Answer

Answer: False. Solution: An elementary event is defined as an event with only one outcome.

Question 51

The theoretical probability of an event is calculated by dividing the number of outcomes favorable to the event by the total number of possible outcomes, assuming all outcomes are equally likely.

Accepted Answer

Answer: True. Solution: The theoretical probability, also known as classical probability, is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes, assuming equally likely outcomes.

Question 52

The probability of an impossible event is 1.

Accepted Answer

Answer: False. Solution: The probability of an impossible event is 0, as there are no favorable outcomes for an impossible event.

Question 53

The sample space for a single coin toss is $\{H, T\}$, where $H$ represents heads and $T$ represents tails.

Accepted Answer

Answer: True. Solution: When a fair coin is tossed, it can land either heads up or tails up, making the sample space $\{H, T\}$.

Question 54

The probability of drawing a red ball from a bag containing 4 red balls and 1 blue ball is 0.5.

Accepted Answer

Answer: False. Solution: The probability of drawing a red ball is calculated as the number of red balls divided by the total number of balls: $\frac{4}{5} = 0.8$.

Question 55

In a bag containing 4 red balls and 1 blue ball, drawing a red ball and a blue ball are equally likely events.

Accepted Answer

Answer: False. Solution: Since there are 4 red balls and only 1 blue ball, drawing a red ball is more likely than drawing a blue ball.

Question 56

In a single throw of a die, the probability of getting a number greater than 4 is $ \frac{1}{3} $.

Accepted Answer

Answer: True. Solution: The possible outcomes when a die is thrown are 1, 2, 3, 4, 5, and 6. The numbers greater than 4 are 5 and 6, giving 2 favorable outcomes. Thus, the probability is $ \frac{2}{6} = \frac{1}{3} $.

Question 57

The sum of the probabilities of all elementary events of an experiment is always less than 1.

Accepted Answer

Answer: False. Solution: The sum of the probabilities of all elementary events of an experiment is 1.

Question 58

If the probability of an event $E$ is $0.7$, then the probability of the complementary event 'not $E$' is $0.3$.

Accepted Answer

Answer: True. Solution: The probability of an event $E$ and its complement 'not $E$' always add up to 1. Therefore, if $P(E) = 0.7$, then $P(	ext{not } E) = 1 - 0.7 = 0.3$.

Question 59

If a die is thrown, the probability of getting a number greater than 6 is 1.

Accepted Answer

Answer: False. Solution: The probability of getting a number greater than 6 on a standard die is 0, as the highest number on a die is 6.

Question 60

The probability of an event that cannot happen is greater than zero.

Accepted Answer

Answer: False. Solution: The probability of an impossible event is 0, as there are no outcomes favorable to such an event.

Question 61

In a single throw of a fair die, the probability of rolling a number greater than 6 is greater than zero.

Accepted Answer

Answer: False. Solution: A fair die has numbers 1 to 6. There is no number greater than 6, so the probability is zero.

Question 62

Empirical probability requires the repetition of experiments to determine the likelihood of an event.

Accepted Answer

Answer: True. Solution: Empirical probability is based on actual outcomes of experiments, which often need to be repeated to gather sufficient data.

Question 63

The probability of drawing a red ball from a bag containing 4 red balls and 1 blue ball is $ \frac{4}{5} $.

Accepted Answer

Answer: True. Solution: The bag contains 4 red balls and 1 blue ball, making a total of 5 balls. The probability of drawing a red ball is $ \frac{4}{5} $ since there are 4 favorable outcomes.

Question 64

The probability of an impossible event is 1.

Accepted Answer

Answer: False. Solution: The probability of an impossible event is 0, not 1. An impossible event is one that cannot occur under any circumstances.

Probability

Learning Objectives

Learning Objectives

Revision Notes & Summary

Chapter Notes

Classical Probability

Complementary Events

Elementary Events

Probability of Sure and Impossible Events

Empirical vs Theoretical Probability

Key Properties

Examples

Important Notes

Exam Tips & Common Mistakes

Common Mistakes & Exam Tips

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Multiple Choice Questions

Q1.A bag contains 3 red balls, 2 white balls, and 4 blue balls. If a ball is drawn at random, what is the probability that the ball drawn is not blue?

Correct Answer: B

Q2.A deck of cards contains 52 cards. If one card is drawn at random, what is the probability that it is not an ace?

Correct Answer: C

Q3.What is the probability of drawing a card that is not an ace from a well-shuffled deck of 52 cards?

Correct Answer: B

Q4.In a theoretical probability scenario, a fair die is rolled once. What is the probability of rolling a number greater than 4?

Correct Answer: B

Q5.A fair die is thrown once. What is the probability of getting an elementary event where the outcome is a number greater than 4?

Correct Answer: A

Q6.In a deck of 52 cards, what is the probability of drawing a card that is not an ace?

Correct Answer: D

Q7.In a deck of 52 cards, what is the probability of drawing a spade?

Correct Answer: A

Q8.A bag contains 4 red balls and 1 blue ball. If a ball is drawn at random, what is the probability that the ball drawn is red?

Correct Answer: D

Q9.In a game, a die is thrown once. What is the probability of getting a number greater than 6?

Correct Answer: A

Q10.If a die is thrown once, what is the probability of getting a number greater than 4?

Correct Answer: B

Q11.In a standard deck of 52 playing cards, what is the probability of drawing an elementary event that is a face card?

Correct Answer: A

Q12.What is the theoretical probability of getting a head when a fair coin is tossed once?

Correct Answer: A

Q13.Suppose a fair die is rolled once. What is the probability of getting a number greater than 5?

Correct Answer: A

Q14.If two dice are thrown simultaneously, what is the probability that the sum of the numbers is 8?

Correct Answer: A

Q15.A bag contains 3 red balls and 5 black balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is neither red nor black?

Correct Answer: B

Q16.A bag contains 3 red balls and 5 black balls. What is the probability of drawing a red ball?

Correct Answer: A

Q17.A bag contains 3 red balls, 5 blue balls, and 2 green balls. If a ball is drawn at random, what is the empirical probability that the ball drawn is red, given that in 10 previous draws, 4 red balls were drawn?

Correct Answer: B

Q18.A standard deck of 52 cards is shuffled and one card is drawn at random. What is the probability that the card drawn is a face card?

Correct Answer: A

Q19.What is the probability of drawing a red face card from a well-shuffled deck of 52 cards?

Correct Answer: A

Q20.Which of the following statements is true regarding the probability of events?

Correct Answer: C

Q21.What is the probability of drawing a red ball from a bag containing 4 red balls and 1 blue ball?

Correct Answer: D

Q22.In a game, a fair coin is tossed three times. What is the probability of getting exactly two heads?

Correct Answer: B

Q23.In a game of chance, a spinner is divided into 8 equal sections numbered 1 to 8. What is the probability that it will land on an odd number?

Correct Answer: A

Q24.A spinner is divided into 8 equal sections numbered 1 to 8. If the spinner is spun once, what is the probability of landing on a number greater than 5?

Correct Answer: A

Q25.If the probability of an event EEE is 0.3, what is the probability of the complementary event E‾\overline{E}E?

Correct Answer: B

Q26.A bag contains 4 red balls and 1 blue ball. If one ball is drawn at random, what is the probability that it is not blue?

Correct Answer: C

Q27.A bag contains 3 blue, 2 white, and 4 red marbles. What is the probability of drawing a white marble?

Correct Answer: B

Q28.When two dice are thrown simultaneously, what is the probability of getting a sum of 8?

Correct Answer: A

Q29.A die is thrown once. What is the probability of getting a prime number?