Question 1

In a random experiment of tossing a coin three times, what is the probability of getting at least two heads?

Accepted Answer

Correct Option: C. Solution: The sample space is $S = \{HHH, HHT, HTH, THH, HTT, THT, TTH, TTT\}$. The favorable outcomes for at least two heads are $\{HHH, HHT, HTH, THH\}$. Thus, $P(	ext{at least two heads}) = \frac{4}{8} = \frac{1}{2}$.

Question 2

What is the sample space for the experiment of tossing a coin twice?

Accepted Answer

Correct Option: B. Solution: The sample space for tossing a coin twice includes all possible outcomes: $HH$, $HT$, $TH$, and $TT$.

Question 3

Consider three events $A$, $B$, and $C$ such that $P(A) = 0.4$, $P(B) = 0.3$, $P(C) = 0.2$, $P(A \cap B) = 0.1$, $P(A \cap C) = 0.05$, $P(B \cap C) = 0.02$, and $P(A \cap B \cap C) = 0.01$. Determine if the events $A$, $B$, and $C$ are mutually exclusive.

Accepted Answer

Correct Option: D. Solution: Events are mutually exclusive if $P(A \cap B) = P(A \cap C) = P(B \cap C) = 0$. Since $P(A \cap B) = 0.1$, $P(A \cap C) = 0.05$, and $P(B \cap C) = 0.02$, they are not mutually exclusive.

Question 4

In a sample space $S = \{1, 2, 3, 4, 5, 6\}$, let $A$ be the event 'getting a prime number'. What is $P(A)$?

Accepted Answer

Correct Option: B. Solution: The prime numbers in the sample space are 2, 3, and 5. Thus, $P(A) = \frac{3}{6} = \frac{1}{3}$.

Question 5

In the experiment of tossing a coin twice, which subset of the sample space corresponds to the event 'second toss is not head'?

Accepted Answer

Correct Option: C. Solution: The subset corresponding to the event 'second toss is not head' is {TH, TT}.

Question 6

In the context of probability, what is an impossible event?

Accepted Answer

Correct Option: A. Solution: An impossible event is represented by the empty set $\Phi$ and has no outcomes in the sample space.

Question 7

In a class of 60 students, 30 opted for NCC, 32 opted for NSS, and 24 opted for both. What is the probability that a randomly selected student has opted for either NCC or NSS?

Accepted Answer

Correct Option: C. Solution: Using the formula $P(A \cup B) = P(A) + P(B) - P(A \cap B)$, we have $P(A \cup B) = \frac{30}{60} + \frac{32}{60} - \frac{24}{60} = \frac{38}{60} = \frac{19}{30}$.

Question 8

Which of the following is a sure event when a die is rolled?

Accepted Answer

Correct Option: B. Solution: A sure event is one that will always occur. Rolling a die will always result in a number less than 7.

Question 9

In a deck of 52 cards, what is the probability of drawing a card that is either a heart or a king?

Accepted Answer

Correct Option: C. Solution: There are 13 hearts and 4 kings in a deck. However, one of the kings is a heart, so $P(	ext{heart} \cup 	ext{king}) = \frac{13 + 4 - 1}{52} = \frac{16}{52} = \frac{4}{13}$.

Question 10

If two events $A$ and $B$ are mutually exclusive, what is the probability of their intersection $A \cap B$?

Accepted Answer

Correct Option: A. Solution: Mutually exclusive events cannot occur simultaneously, hence $P(A \cap B) = 0$.

Question 11

If A and B are two events such that A = {2, 3, 5} and B = {1, 3, 5}, what is the event 'A but not B'?

Accepted Answer

Correct Option: D. Solution: The event 'A but not B' is represented by the set difference A - B, which is {2}.

Question 12

In a die rolling experiment, let $A$ be the event 'getting a prime number' and $B$ be the event 'getting an odd number'. What is the probability of the event $A \cap B$?

Accepted Answer

Correct Option: B. Solution: The prime numbers on a die are $2, 3, 5$. The odd numbers are $1, 3, 5$. Thus, $A \cap B = \{3, 5\}$, giving $P(A \cap B) = \frac{2}{6} = \frac{1}{3}$.

Question 13

If $P(A) = 0.4$, what is the probability of the complement of event $A$?

Accepted Answer

Correct Option: A. Solution: The probability of the complement of an event $A$ is given by $P(A') = 1 - P(A)$. Therefore, $P(A') = 1 - 0.4 = 0.6$.

Question 14

What is the probability of the event 'A or B' if $P(A) = 0.5$, $P(B) = 0.4$, and $P(A \cap B) = 0.2$?

Accepted Answer

Correct Option: B. Solution: The probability of 'A or B' is calculated using the formula $P(A \cup B) = P(A) + P(B) - P(A \cap B)$. Substituting the given values, $P(A \cup B) = 0.5 + 0.4 - 0.2 = 0.7$.

Question 15

If $P(A) = 0.6$ and $P(	ext{not } A) = 0.4$, what is the probability of $A$ and its complement being mutually exclusive?

Accepted Answer

Correct Option: D. Solution: By definition, an event and its complement are always mutually exclusive, so the probability is 1.

Question 16

Given two events $A$ and $B$ with $P(A) = 0.5$, $P(B) = 0.3$, and $P(A \cap B) = 0.1$, what is $P(A \cup B)$?

Accepted Answer

Correct Option: B. Solution: The probability of the union of two events $A$ and $B$ is given by $P(A \cup B) = P(A) + P(B) - P(A \cap B)$. Therefore, $P(A \cup B) = 0.5 + 0.3 - 0.1 = 0.7$.

Question 17

In a sample space $S = \{HH, HT, TH, TT\}$, what is the probability of the event 'not A' if $A = \{HH, HT\}$?

Accepted Answer

Correct Option: A. Solution: The event 'not A' corresponds to the outcomes not in $A$, which are $\{TH, TT\}$. There are 2 favorable outcomes out of 4 possible outcomes, so the probability is $\frac{2}{4} = \frac{1}{2}$.

Question 18

In a lottery where a person chooses six different natural numbers at random from 1 to 20, what is the probability of winning the prize if these six numbers match with the six numbers already fixed by the lottery committee?

Accepted Answer

Correct Option: A. Solution: The number of ways to choose 6 numbers out of 20 is $\binom{20}{6} = 38760$. Thus, the probability of winning is $\frac{1}{38760}$.

Question 19

If a die is rolled, what is the probability of getting a number less than 4?

Accepted Answer

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

Question 20

Consider the experiment of rolling a die. Let event $A$ be 'the number is a multiple of 7'. What is the probability of event $A$ occurring?

Accepted Answer

Correct Option: A. Solution: Since no number on a standard die is a multiple of 7, the event $A$ is an impossible event, and its probability is 0.

Question 21

Given a sample space $S = \{ w_1, w_2, w_3, w_4 \}$ with $P(w_1) = 0.25$, $P(w_2) = 0.25$, $P(w_3) = 0.25$, and $P(w_4) = 0.25$, what is the probability of the event $B = \{ w_2, w_3 \}$?

Accepted Answer

Correct Option: B. Solution: The probability of event $B$ is $P(B) = P(w_2) + P(w_3) = 0.25 + 0.25 = 0.5$.

Question 22

A bag contains 4 red, 3 blue, and 2 yellow discs. If a disc is drawn at random, what is the probability that it is either red or blue?

Accepted Answer

Correct Option: C. Solution: The event 'red or blue' has 7 favorable outcomes out of 9. Thus, $P(	ext{red or blue}) = \frac{7}{9}$.

Question 23

A bag contains 5 red, 4 blue, and 3 green balls. If 3 balls are drawn at random, what is the probability that all of them are red?

Accepted Answer

Correct Option: A. Solution: The number of ways to choose 3 red balls from 5 is $\binom{5}{3} = 10$. The total number of ways to choose any 3 balls from 12 is $\binom{12}{3} = 220$. Thus, the probability is $\frac{10}{220} = \frac{1}{22}$.

Question 24

In the context of probability, which of the following sets represents an impossible event when rolling a die?

Accepted Answer

Correct Option: A. Solution: The set $\{7\}$ is an impossible event because 7 is not a possible outcome when rolling a standard die.

Question 25

Consider a sample space $S = \{HH, HT, TH, TT\}$ for tossing two coins. What is the probability of the event $E$ where 'the second toss is not a head'?

Accepted Answer

Correct Option: B. Solution: The event $E = \{HT, TT\}$, which are 2 outcomes out of 4. Thus, $P(E) = \frac{2}{4} = \frac{1}{2}$.

Question 26

In a lottery with 10,000 tickets, what is the probability that buying 10 tickets will not win any prize if 10 prizes are awarded?

Accepted Answer

Correct Option: B. Solution: The probability of not winning with one ticket is $\frac{9990}{10000}$. For 10 tickets, $P(	ext{no prize}) = \left(\frac{9990}{10000}ight)^{10} \approx 0.99$.

Question 27

In a sample space $S = \{HH, HT, TH, TT\}$, which of the following represents the event 'at least one head appears'?

Accepted Answer

Correct Option: A. Solution: The event 'at least one head appears' includes all outcomes except $TT$, which are $\{HH, HT, TH\}$.

Question 28

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

Accepted Answer

Correct Option: A. Solution: The sample space is $S = \{1, 2, 3, 4, 5, 6\}$. The event $E$ is getting a number less than 4, which is $E = \{1, 2, 3\}$. Therefore, $P(E) = \frac{n(E)}{n(S)} = \frac{3}{6} = \frac{1}{3}$.

Question 29

Consider the events A: 'a number less than 4 appears' and B: 'a number greater than 2 but less than 5 appears' when a die is rolled. Are these events mutually exclusive?

Accepted Answer

Correct Option: B. Solution: The events A = {1, 2, 3} and B = {3, 4} are not mutually exclusive because they share the common outcome 3.

Question 30

What is the probability of the empty set $\Phi$ in the axiomatic approach?

Accepted Answer

Correct Option: A. Solution: In the axiomatic approach, the probability of the empty set $\Phi$ is 0.

Question 31

Consider the experiment of tossing a coin twice. What is the probability of getting exactly one head?

Accepted Answer

Correct Option: B. Solution: The sample space is $S = \{HH, HT, TH, TT\}$. The event of getting exactly one head is $E = \{HT, TH\}$. Therefore, $P(E) = \frac{n(E)}{n(S)} = \frac{2}{4} = \frac{1}{2}$.

Question 32

If $P(A) = 0.5$, $P(B) = 0.4$, and $P(A \cap B) = 0.2$, what is $P(A \cup B)$?

Accepted Answer

Correct Option: B. Solution: Using the formula $P(A \cup B) = P(A) + P(B) - P(A \cap B)$, we get $P(A \cup B) = 0.5 + 0.4 - 0.2 = 0.7$.

Question 33

Consider two events $A$ and $B$ in a sample space $S$. If $P(A) = 0.4$, $P(B) = 0.5$, and $P(A \cup B) = 0.7$, what is $P(A \cap B)$?

Accepted Answer

Correct Option: B. Solution: Using the formula $P(A \cup B) = P(A) + P(B) - P(A \cap B)$, we have $0.7 = 0.4 + 0.5 - P(A \cap B)$, thus $P(A \cap B) = 0.2$.

Question 34

In an experiment of rolling a die, let event $A$ be 'a number less than 4 appears' and event $B$ be 'an even number appears'. What is the probability of the union of events $A$ and $B$, $P(A \cup B)$?

Accepted Answer

Correct Option: B. Solution: The sample space $S = \{1, 2, 3, 4, 5, 6\}$. Event $A = \{1, 2, 3\}$ and event $B = \{2, 4, 6\}$. The union $A \cup B = \{1, 2, 3, 4, 6\}$. Thus, $P(A \cup B) = \frac{5}{6}$.

Question 35

Which of the following assignments of probabilities is valid for a sample space $S = \{w_1, w_2, w_3, w_4, w_5, w_6\}$?

Accepted Answer

Correct Option: A. Solution: The assignment in option A is valid because each probability is between 0 and 1, and their sum is 1.

Question 36

Consider a sample space $S = \{ w_1, w_2, w_3, w_4 \}$ with probabilities assigned as $P(w_1) = 0.2$, $P(w_2) = 0.3$, $P(w_3) = 0.4$, and $P(w_4) = 0.2$. Are these assignments valid according to the axiomatic approach to probability?

Accepted Answer

Correct Option: B. Solution: The sum of probabilities $P(w_1) + P(w_2) + P(w_3) + P(w_4) = 0.2 + 0.3 + 0.4 + 0.2 = 1.1$, which is greater than 1. Therefore, the assignment is not valid.

Question 37

If $E$ and $F$ are mutually exclusive events, what is $P(E \cup F)$?

Accepted Answer

Correct Option: A. Solution: For mutually exclusive events $E$ and $F$, $P(E \cup F) = P(E) + P(F)$ as per the axiomatic approach.

Question 38

In the experiment of tossing a coin twice, which of the following sets of events are exhaustive?

Accepted Answer

Correct Option: A. Solution: Events are exhaustive if they cover all possible outcomes. Option A covers all possibilities when a coin is tossed twice.

Question 39

If two dice are thrown, what is the probability of the event where the sum is either a multiple of 3 or greater than 10?

Accepted Answer

Correct Option: C. Solution: The event 'sum is a multiple of 3' has outcomes $\{3, 6, 9, 12\}$ and 'sum greater than 10' has outcomes $\{11, 12\}$. Using inclusion-exclusion, $P(A \cup B) = P(A) + P(B) - P(A \cap B) = \frac{12}{36} + \frac{3}{36} - \frac{1}{36} = \frac{14}{36} = \frac{7}{18}$.

Question 40

A committee of two persons is selected from two men and two women. What is the probability that the committee will have one man and one woman?

Accepted Answer

Correct Option: C. Solution: The total number of ways to choose 2 people from 4 is $\binom{4}{2} = 6$. The number of ways to choose 1 man and 1 woman is $\binom{2}{1} 	imes \binom{2}{1} = 4$. Therefore, the probability is $\frac{4}{6} = \frac{2}{3}$.

Question 41

What is the probability that in a group of 5 people, at least two share the same birthday, assuming 365 days in a year?

Accepted Answer

Correct Option: A. Solution: The probability that no two people share a birthday is $\frac{365}{365} 	imes \frac{364}{365} 	imes \frac{363}{365} 	imes \frac{362}{365} 	imes \frac{361}{365} \approx 0.973$. Therefore, the probability that at least two share a birthday is $1 - 0.973 = 0.027$.

Question 42

Given a sample space $S = \{w_1, w_2, ..., w_n\}$, which condition must hold for the probabilities of elementary events?

Accepted Answer

Correct Option: A. Solution: The sum of the probabilities of all elementary events in a sample space must equal 1.

Question 43

If $P(A) = 0.4$ and $P(B) = 0.5$ for two mutually exclusive events $A$ and $B$, what is $P(A \cup B)$?

Accepted Answer

Correct Option: A. Solution: Since $A$ and $B$ are mutually exclusive, $P(A \cup B) = P(A) + P(B) = 0.4 + 0.5 = 0.9$.

Question 44

What is the probability of the event $A \cup B \cup C$ if $P(A) = 0.3$, $P(B) = 0.4$, $P(C) = 0.2$, $P(A \cap B) = 0.1$, $P(B \cap C) = 0.05$, $P(A \cap C) = 0.05$, and $P(A \cap B \cap C) = 0.02$?

Accepted Answer

Correct Option: B. Solution: The probability of the union of three events is given by the formula $P(A \cup B \cup C) = P(A) + P(B) + P(C) - P(A \cap B) - P(B \cap C) - P(A \cap C) + P(A \cap B \cap C)$. Substituting the given values, we have $P(A \cup B \cup C) = 0.3 + 0.4 + 0.2 - 0.1 - 0.05 - 0.05 + 0.02 = 0.92$.

Question 45

Which of the following statements is true for mutually exclusive events $A$ and $B$?

Accepted Answer

Correct Option: B. Solution: For mutually exclusive events $A$ and $B$, $P(A \cap B) = 0$ and $P(A \cup B) = P(A) + P(B)$. Therefore, option b is correct.

Question 46

A committee of 3 members is to be formed from a group of 5 men and 4 women. What is the probability that the committee will consist of 2 men and 1 woman?

Accepted Answer

Correct Option: B. Solution: The number of ways to choose 2 men from 5 is $\binom{5}{2} = 10$. The number of ways to choose 1 woman from 4 is $\binom{4}{1} = 4$. The total number of ways to choose 3 people from 9 is $\binom{9}{3} = 84$. Thus, the probability is $\frac{10 	imes 4}{84} = \frac{40}{84} = \frac{10}{21}$.

Question 47

Consider a sample space $S = \{1, 2, 3, 4, 5, 6\}$ for a die roll. Let $A$ be the event 'getting a number less than 4' and $B$ be the event 'getting an even number'. Using the axiomatic approach to probability, what is $P(A \cup B)$?

Accepted Answer

Correct Option: C. Solution: The event $A = \{1, 2, 3\}$ and the event $B = \{2, 4, 6\}$. The union $A \cup B = \{1, 2, 3, 4, 6\}$, which contains 5 outcomes. Since there are 6 possible outcomes in $S$, $P(A \cup B) = \frac{5}{6} = 0.83$.

Question 48

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

Accepted Answer

Correct Option: C. Solution: The sample space has 36 outcomes. The favorable outcomes for the sum greater than 8 are $\{(3,6), (4,5), (4,6), (5,4), (5,5), (5,6), (6,3), (6,4), (6,5), (6,6)\}$, totaling 10 outcomes. Therefore, $P(E) = \frac{10}{36} = \frac{5}{18}$.

Question 49

Which of the following is an axiom of probability?

Accepted Answer

Correct Option: A. Solution: The axiomatic approach to probability states that for any event $E$, $P(E) \geq 0$.

Question 50

If the probability of event $A$ is $0.7$ and the probability of event $B$ is $0.6$, and $A$ and $B$ are mutually exclusive, what is the probability of $A \cup B$?

Accepted Answer

Correct Option: C. Solution: For mutually exclusive events, $P(A \cup B) = P(A) + P(B) = 0.7 + 0.6 = 1.3$. However, since probabilities cannot exceed 1, the maximum value is 1.0.

Question 51

If a die is rolled, what is the probability of getting a number that is either a prime or greater than 4?

Accepted Answer

Correct Option: B. Solution: The prime numbers on a die are $\{2, 3, 5\}$ and numbers greater than 4 are $\{5, 6\}$. The union of these sets is $\{2, 3, 5, 6\}$. Thus, $P(	ext{prime or > 4}) = \frac{4}{6} = \frac{2}{3}$.

Question 52

What is the probability of not drawing an ace from a standard deck of 52 cards?

Accepted Answer

Correct Option: A. 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 53

Given three events $A$, $B$, and $C$ with probabilities $P(A) = 0.3$, $P(B) = 0.5$, and $P(C) = 0.4$, and knowing that $P(A \cap B) = 0.1$, $P(A \cap C) = 0.2$, $P(B \cap C) = 0.15$, and $P(A \cap B \cap C) = 0.05$, calculate $P(A \cup B \cup C)$.

Accepted Answer

Correct Option: A. Solution: Using the formula $P(A \cup B \cup C) = P(A) + P(B) + P(C) - P(A \cap B) - P(A \cap C) - P(B \cap C) + P(A \cap B \cap C)$, we have $P(A \cup B \cup C) = 0.3 + 0.5 + 0.4 - 0.1 - 0.2 - 0.15 + 0.05 = 0.95$.

Question 54

If a die is thrown, what is the event of getting a number less than 4?

Accepted Answer

Correct Option: A. Solution: The event of getting a number less than 4 includes the outcomes $1$, $2$, and $3$.

Question 55

In a lottery, a person chooses six different natural numbers at random from 1 to 20. If these six numbers match with the six numbers already fixed by the lottery committee, he wins the prize. What is the probability of winning the prize?

Accepted Answer

Correct Option: A. Solution: The probability of choosing the correct 6 numbers out of 20 is $\frac{1}{\binom{20}{6}} = \frac{1}{38760}$.

Question 56

Which of the following pairs of events are mutually exclusive when a die is rolled?

Accepted Answer

Correct Option: A. Solution: Events A and B are mutually exclusive if they cannot occur simultaneously. For option A, an odd number and an even number cannot appear at the same time.

Question 57

A committee of two persons is selected from two men and two women. What is the probability that the committee will have one man?

Accepted Answer

Correct Option: A. Solution: One man in the committee means there is one woman. One man out of 2 can be selected in $\binom{2}{1}$ ways and one woman out of 2 can be selected in $\binom{2}{1}$ ways. Together they can be selected in $\binom{2}{1} 	imes \binom{2}{1} = 4$ ways. Total ways to select 2 people from 4 is $\binom{4}{2} = 6$. Thus, the probability is $\frac{4}{6} = \frac{2}{3}$.

Question 58

Consider the events $A$ and $B$ in a sample space $S$ such that $P(A) = 0.4$, $P(B) = 0.5$, and $P(A \cap B) = 0.1$. Calculate $P(A' \cup B')$, where $A'$ and $B'$ are the complements of $A$ and $B$ respectively.

Accepted Answer

Correct Option: D. Solution: Using the formula $P(A' \cup B') = 1 - P(A \cap B)$, we find $P(A' \cup B') = 1 - 0.1 = 0.9$.

Question 59

Consider the experiment of rolling a die. Let event A be 'a number less than 4 appears' and event B be 'an even number appears'. Are A and B mutually exclusive?

Accepted Answer

Correct Option: B. Solution: Event A = {1, 2, 3} and Event B = {2, 4, 6}. Since 2 is common to both events, A and B are not mutually exclusive.

Question 60

A box contains 3 red balls and 2 blue balls. Two balls are drawn at random. What is the probability that both balls are red if the events are mutually exclusive?

Accepted Answer

Correct Option: D. Solution: Mutually exclusive events cannot happen simultaneously. If both balls are red, it is not a mutually exclusive event.

Question 61

In the experiment of tossing a coin twice, which of the following sets of events are mutually exclusive and exhaustive?

Accepted Answer

Correct Option: A. Solution: The events A = {TT}, B = {HT, TH}, and C = {HH} cover all possible outcomes and are mutually exclusive.

Question 62

A sample space $S = \{ w_1, w_2, w_3 \}$ has probabilities $P(w_1) = 0.5$, $P(w_2) = 0.3$, and $P(w_3) = 0.2$. If a new event $A = \{ w_1, w_3 \}$ is defined, what is the probability of event $A$?

Accepted Answer

Correct Option: B. Solution: The probability of event $A$ is $P(A) = P(w_1) + P(w_3) = 0.5 + 0.2 = 0.7$.

Question 63

If two dice are thrown, what is the probability that the sum of the numbers is at least 10?

Accepted Answer

Correct Option: A. Solution: The possible sums of at least 10 are $\{10, 11, 12\}$. The favorable outcomes are $\{(4,6), (5,5), (5,6), (6,4), (6,5), (6,6)\}$, totaling 6 outcomes. Thus, $P(	ext{sum} \geq 10) = \frac{6}{36} = \frac{1}{6}$.

Question 64

If two events are mutually exclusive, they cannot occur simultaneously.

Accepted Answer

Answer: True. Solution: Mutually exclusive events are defined as events that cannot occur at the same time. This means that if one event occurs, the other cannot.

Probability

Learning Objectives

Learning Objectives

Revision Notes & Summary

Chapter Notes

Sample Space and Events

Algebra of Events

Axiomatic Probability

Probability of Events

Mutually Exclusive and Exhaustive Events

Probability of Union and Complement of Events

Equally Likely Outcomes and Classical Probability

Valid Assignment of Probabilities

Combinatorics-Based Probability Problems

Probability of Three Events

Exam Tips & Common Mistakes

Common Mistakes & Exam Tips

Sample Space and Events

Algebra of Events

Axiomatic Probability

Probability of Events

Mutually Exclusive and Exhaustive Events

Probability of Union and Complement of Events

Equally Likely Outcomes and Classical Probability

Valid Assignment of Probabilities

Combinatorics-Based Probability Problems

Probability of Three Events

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Multiple Choice Questions

Q1.In a random experiment of tossing a coin three times, what is the probability of getting at least two heads?

Correct Answer: C

Q2.What is the sample space for the experiment of tossing a coin twice?

Correct Answer: B

Correct Answer: D

Q4.In a sample space S={1,2,3,4,5,6}S = \{1, 2, 3, 4, 5, 6\}S={1,2,3,4,5,6}, let AAA be the event 'getting a prime number'. What is P(A)P(A)P(A)?

Correct Answer: B

Q5.In the experiment of tossing a coin twice, which subset of the sample space corresponds to the event 'second toss is not head'?

Correct Answer: C

Q6.In the context of probability, what is an impossible event?

Correct Answer: A

Q7.In a class of 60 students, 30 opted for NCC, 32 opted for NSS, and 24 opted for both. What is the probability that a randomly selected student has opted for either NCC or NSS?

Correct Answer: C

Q8.Which of the following is a sure event when a die is rolled?

Correct Answer: B

Q9.In a deck of 52 cards, what is the probability of drawing a card that is either a heart or a king?

Correct Answer: C

Q10.If two events AAA and BBB are mutually exclusive, what is the probability of their intersection A∩BA \cap BA∩B?

Correct Answer: A

Q11.If A and B are two events such that A = {2, 3, 5} and B = {1, 3, 5}, what is the event 'A but not B'?

Correct Answer: D

Q12.In a die rolling experiment, let AAA be the event 'getting a prime number' and BBB be the event 'getting an odd number'. What is the probability of the event A∩BA \cap BA∩B?

Correct Answer: B

Q13.If P(A)=0.4P(A) = 0.4P(A)=0.4, what is the probability of the complement of event AAA?

Correct Answer: A

Q14.What is the probability of the event 'A or B' if P(A)=0.5P(A) = 0.5P(A)=0.5, P(B)=0.4P(B) = 0.4P(B)=0.4, and P(A∩B)=0.2P(A \cap B) = 0.2P(A∩B)=0.2?

Correct Answer: B

Q15.If P(A)=0.6P(A) = 0.6P(A)=0.6 and P(not A)=0.4P(\text{not } A) = 0.4P(not A)=0.4, what is the probability of AAA and its complement being mutually exclusive?

Correct Answer: D

Q16.Given two events AAA and BBB with P(A)=0.5P(A) = 0.5P(A)=0.5, P(B)=0.3P(B) = 0.3P(B)=0.3, and P(A∩B)=0.1P(A \cap B) = 0.1P(A∩B)=0.1, what is P(A∪B)P(A \cup B)P(A∪B)?

Correct Answer: B

Q17.In a sample space S={HH,HT,TH,TT}S = \{HH, HT, TH, TT\}S={HH,HT,TH,TT}, what is the probability of the event 'not A' if A={HH,HT}A = \{HH, HT\}A={HH,HT}?

Correct Answer: A

Q18.In a lottery where a person chooses six different natural numbers at random from 1 to 20, what is the probability of winning the prize if these six numbers match with the six numbers already fixed by the lottery committee?

Correct Answer: A

Q19.If a die is rolled, what is the probability of getting a number less than 4?

Correct Answer: A

Q20.Consider the experiment of rolling a die. Let event AAA be 'the number is a multiple of 7'. What is the probability of event AAA occurring?

Correct Answer: A

Correct Answer: B

Q22.A bag contains 4 red, 3 blue, and 2 yellow discs. If a disc is drawn at random, what is the probability that it is either red or blue?

Correct Answer: C

Q23.A bag contains 5 red, 4 blue, and 3 green balls. If 3 balls are drawn at random, what is the probability that all of them are red?

Correct Answer: A

Q24.In the context of probability, which of the following sets represents an impossible event when rolling a die?