Assertion and Reason Questions For Class 9 Maths Chapter 7: The Mathematics of Maybe: Introduction to Probability

Assertion and Reason questions for Class 9 Maths Chapter 7, The Mathematics of Maybe: Introduction to Probability are available in this Maths. These questions are helpful to understand the chapter and solve the probability-based questions with ease. The article helps the students to understand the important concepts related to chance, probability, simple probability and the type of questions expected in the chapter. Our subject matter experts has designed complete solutions according to CBSE Syllabus and NCERT Books. This material helps the students to revise the chapter easily and gain confidence to perform in final examination. The free downloadable PDF is also available for quick revision and practice.

Assertion and Reason Questions on Class 9 Maths Chapter 7: The Mathematics of Maybe: Introduction to Probability

Directions: In each question below, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option:

(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.

Q1:
Assertion (A): Probability measures how likely an event is to occur and is expressed on a scale from 0 to 1.
Reason (R): A probability of 0 means the event is impossible, while a probability of 1 means the event is certain.
Answer: (a) Both A and R are true, and R correctly explains A.
Explanation: Probability is measured on a scale from 0 to 1. The values 0 and 1 represent the two extreme cases: an impossible event and a certain event. So, R correctly explains A.

Q2:
Assertion (A): Experimental probability and theoretical probability are always equal.
Reason (R): Experimental probability depends on actual observations.
Answer: (c) A is true but R is false.
Explanation: Experimental probability may differ from theoretical probability because of variations in the actual experiment.

Q3:
Assertion (A): The probability of flipping a fair coin and getting heads is 0.5, meaning it is equally likely to get heads or tails.
Reason (R): A fair coin is symmetrical and unbiased, so there is no reason for it to land on one side more often than the other.
Answer: (a) Both A and R are true, and R correctly explains A.
Explanation: Both statements are true. Since the coin is fair, each outcome, heads or tails, has a probability of 1/2. R gives the reason behind A.

Q4:
Assertion (A): Rain is considered a random event.
Reason (R): Rainfall depends on many complex atmospheric factors, such as temperature, humidity, wind, and pressure, so exact prediction with total certainty is impossible.
Answer: (a) Both A and R are true, and R correctly explains A.
Explanation: Both statements are true, and R gives the direct explanation for A.

Q5:
Assertion (A): If a die is rolled 50 times and lands on 4 exactly 8 times, the experimental probability of rolling a 4 is 8/50 = 0.16.
Reason (R): The theoretical probability of rolling a 4 on a fair 6-sided die is 1/6 ≈ 0.167, which equals the experimental probability in this case.
Answer: (c) A is true but R is false.
Explanation: A is true. 8/50 = 0.16 is correct. R is false because the theoretical probability of rolling a 4 on a fair die is 1/6 ≈ 0.167, but this is not equal to the experimental probability 0.16. They are close, but not exactly the same.

Q6:
Assertion (A): A letter is picked at random from the word "PROBABILITY". The probability of picking the letter B is 2/11.
Reason (R): The word "PROBABILITY" has 11 letters in total, and the letter B appears exactly twice in the word.
Answer: (a) Both A and R are true, and R correctly explains A.
Explanation: P(B)=number of B's/total letters=211≈0.182. P(B)=total letters/number of B’s​=112​≈0.182. Both A and R are correct, and R directly explains how A is obtained.

Q7:
Assertion (A): The sample space S = {0, 1, 2, 3} correctly describes the possible number of heads when three coins are tossed.
Reason (R): When three coins are tossed, the only possible counts of heads are 0, 1, 2, or 3, with no other values possible.
Answer: (a) Both A and R are true, and R correctly explains A.
Explanation: S = {0, 1, 2, 3} is the correct sample space for the number of heads. You can get 0 heads, 1 head, 2 heads, or 3 heads, and no other number is possible. R correctly explains the range of outcomes in A.

Q8:
Assertion (A): If a fair coin has come up heads six times in a row, the probability of getting tails on the next flip is greater than 1/2.
Reason (R): After six consecutive heads, tails is 'overdue', so the coin is more likely to land on tails to balance out the results.
Answer: (d)
Explanation: A is false because the probability of getting tails on the next toss is still exactly 1/2, not greater. R is also false because it reflects the gambler’s fallacy, which is the mistaken belief that past results change future outcomes. Therefore, both A and R are incorrect.

Q9:
Assertion (A): The probability of getting a prime number on a die is 1/3.
Reason (R): Prime numbers on a die are 2, 3, and 5.
Answer: C
Explanation: There are 3 prime numbers out of 6 outcomes, so the probability is 3/6 = 1/2, not 1/3.

Q10:
Assertion (A): For a survey of 50 students, where 20 prefer mango, the estimated number of students in a school of 1500 who prefer mango is approximately 600.
Reason (R): Statistical probability derived from the sample (P=20/50=0.4) is applied to the full population: 0.4×1500=600.
Answer: (a)
Explanation: A and R are both true, and R is the calculation that gives the result in A.

Q11:
Assertion (A): The probability of getting a number greater than 6 on a standard 6-sided die is 0.
Reason (R): A standard die only has the numbers 1 through 6 on its faces, so getting a number greater than 6 is impossible.
Answer: (a)
Explanation: Both statements are true, and R explains A perfectly.

Q12:
Assertion (A): The probability of drawing any number from 2 to 10 from a standard deck of 52 playing cards is more likely than not, meaning the probability is greater than 0.5.
Reason (R): In a standard deck of 52 cards, there are 36 cards with numbers from 2 to 10, with four cards each for numbers 2 through 10.
Answer: (a)
Explanation: Both A and R are true, and R correctly explains A.

Q13:
Assertion (A): If the probability of an event is 1, then the event is certain to occur.
Reason (R): Probability cannot exceed 1.
Answer: (B)
Explanation: Both statements are true, but R does not explain why the event is certain.

Q14:
Assertion (A): Tossing a coin is a random experiment because you cannot predict with certainty which outcome, heads or tails, will occur on any single toss.
Reason (R): In a random experiment, all possible outcomes are known in advance, but no single outcome can be predicted before the experiment is performed.
Answer: (a)
Explanation: Both statements are true, and R gives the definition of a random experiment.

Q15:
Assertion (A): For the experiment of rolling a 6-sided die, the event “getting a number greater than 4” is E = {5,6}.
Reason (R): The sample space is S={1,2,3,4,5,6}, and only the numbers 5 and 6 satisfy the condition “greater than 4.”
Answer: (a)
Explanation: The event E={5,6} is correct because only 5 and 6 are greater than 4. That gives 2 favourable outcomes out of 6, so P(E)=2/6=1/3. R correctly identifies the favourable outcomes and explains A.

Download the free PDF of Assertion and Reason Questions on Chapter 7: The Mathematics of Maybe: Introduction to Probability for Class 9 here for quick revision and practice.

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