CBSE-Class-10-Maths-Assertion-and-Reason-Chapter-15-Probability

Class 10^th Maths Chapter Assertion and Reason Questions

Question 1

Assertion (A): The probability of an event ranges from 0 to 1.
Reason (R): A probability of 0 means the event cannot occur, while 1 means it will definitely occur.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: This is a fundamental property of probability, ensuring clarity about the likelihood of events.

Question 2

Assertion (A): The sum of probabilities of all possible outcomes of a random experiment is 1.
Reason (R): This is because all outcomes together account for the entire sample space.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: The total probability must equal 1, representing certainty that one of the outcomes will occur.

Question 3

Assertion (A): An event that cannot happen is called an impossible event.
Reason (R): The probability of an impossible event is 0.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: An impossible event has a probability of zero, clearly defining its nature.

Question 4

Assertion (A): A fair coin has a probability of 0.5 for landing on heads.
Reason (R): The coin has two equally likely outcomes: heads and tails.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: Since there are two possible outcomes, the probability of heads is indeed 0.5.

Question 5

Assertion (A): The probability of rolling a 3 on a standard six-sided die is $\frac{1}{6}$ .
Reason (R): There are six equally likely outcomes when rolling a die.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: Each face of the die has an equal chance of landing face up, thus $\frac{1}{6}$ for each number.

Question 6

Assertion (A): The complement of an event A is denoted as $A'$ .
Reason (R): The complement of an event consists of all outcomes not in A.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: The complement indeed contains all outcomes that do not belong to event A.

Question 7

Assertion (A): The probability of an event A occurring plus the probability of it not occurring equals 1.
Reason (R): This is because A and its complement are the only two possible outcomes.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: This reflects the definition of complementary events in probability.

Question 8

Assertion (A): If two events are independent, the occurrence of one does not affect the probability of the other.
Reason (R): This means $P(A \cap B) = P(A) \times P(B)$ .

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: This definition characterizes independent events in probability.

Question 9

Assertion (A): The probability of rolling an even number on a standard six-sided die is $\frac{1}{3}$ .
Reason (R): The even numbers on a die are 2, 4, and 6.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: B) Both A and R are true, but R is not the correct explanation of A.
Explanation: The probability should be $\frac{3}{6} = \frac{1}{2}$ since there are three even outcomes.

Question 10

Assertion (A): The probability of an event can be expressed as a fraction, decimal, or percentage.
Reason (R): All forms represent the same value but in different formats.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: The representation of probability can vary while still conveying the same information.

Question 11

Assertion (A): If $P(A) = 0.3$ , then $P(A') = 0.7$ .
Reason (R): The sum of probabilities of an event and its complement must equal 1.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: This follows the rule of complementary probabilities.

Question 12

Assertion (A): Theoretical probability is based on the possible outcomes of an event.
Reason (R): It is calculated using the formula $P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$ .

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: Theoretical probability indeed relies on the analysis of outcomes.

Question 13

Assertion (A): Experimental probability is calculated based on the actual results of an experiment.
Reason (R): It is computed as $P(E) = \frac{\text{Number of times event occurs}}{\text{Total number of trials}}$ .

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: This defines how experimental probability is derived from trials.

Question 14

Assertion (A): If two events A and B are mutually exclusive, $P(A \cap B) = 0$ .
Reason (R): Mutually exclusive events cannot occur at the same time.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: This is the defining characteristic of mutually exclusive events.

Question 15

Assertion (A): The probability of getting at least one head in three tosses of a fair coin is less than 1.
Reason (R): It is possible to get no heads at all (all tails).

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: Although it’s less than 1, the probability of getting at least one head is actually $\frac{7}{8}$ .

Question 16

Assertion (A): The sample space of an experiment consists of all possible outcomes.
Reason (R): The sample space must be defined clearly before calculating probabilities.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: Clearly defining the sample space is crucial for accurate probability calculations.

Question 17

Assertion (A): In a single coin toss, the probability of getting tails is $\frac{1}{2}$ .
Reason (R): A coin has two faces, heads and tails, which are equally likely.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: Each outcome has an equal probability of occurring in a fair coin toss.

Question 18

Assertion (A): The probability of an event is a number between 0 and 1, inclusive.
Reason (R): This means probabilities can also be expressed as percentages from 0% to 100%.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: The numerical range of probability can be translated into percentage form.

Question 19

Assertion (A): If two events are independent, the occurrence of one event increases the likelihood of the other event occurring.
Reason (R): Independence means that the events have no effect on each other.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: D) A is false, but R is true.
Explanation: If two events are independent, the occurrence of one does not affect the probability of the other.

Question 20

Assertion (A): The probability of selecting a red card from a standard deck of cards is $\frac{1}{2}$ .
Reason (R): A standard deck has 52 cards, with 26 being red.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: There are 26 red cards (hearts and diamonds) out of 52 total cards.

Question 21

Assertion (A): The experimental probability of an event is often different from its theoretical probability due to chance variations.
Reason (R): Experimental probability is based on actual trials and may be influenced by random errors.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: Randomness in trials can lead to discrepancies between experimental and theoretical probabilities.

Question 22

Assertion (A): The probability of an event A plus the probability of its complement A' equals 1.
Reason (R): This reflects the certainty of outcomes in the sample space.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: This is a fundamental property of probability, affirming that one of the two events must occur.

Question 23

Assertion (A): If the probability of event A is $P(A) = 0.8$ , then the probability of the complement of A is $P(A') = 0.2$ .
Reason (R): The complement of an event accounts for all outcomes not included in A.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: This follows from the complementary probability rule $P(A') = 1 - P(A)$ .

Question 24

Assertion (A): The sample space for rolling two dice consists of 36 possible outcomes.
Reason (R): Each die has 6 faces, resulting in $6 \times 6 = 36$ combinations.

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: A) Both A and R are true, and R is the correct explanation of A.
Explanation: The total number of combinations when rolling two dice is accurately represented by $6 \times 6 = 36$ .

Question 25

Assertion (A): The probability of drawing a face card from a standard deck of cards is $\frac{1}{13}$ .
Reason (R): A standard deck has 12 face cards (Jack, Queen, King of each suit).

A) Both A and R are true, and R is the correct explanation of A.
B) Both A and R are true, but R is not the correct explanation of A.
C) A is true, but R is false.
D) A is false, but R is true.
Answer: D) A is false, but R is true.
Explanation: The probability of drawing a face card is actually $\frac{12}{52} = \frac{3}{13}$ .

Chapter 15 Probability

Class 10th Maths Chapter Assertion and Reason Questions