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NCERT Class 9 Mathematics Exercise Set 7.2 Solutions: The Mathematics of Maybe: Introduction to Probability
AI-written, checked on 23 Oct 2026
Solutions written by Shishya, checked — not the board's official answers
Step-by-step working for every question of Exercise Set 7.2 in NCERT's Class 9 Mathematics book, chapter “The Mathematics of Maybe: Introduction to Probability”, written by Shishya. Each question is in our own short words; open the NCERT chapter for the exact wording and figures.
How these were checked: the solutions were drafted with AI and then read and corrected on 23 Oct 2026. Every numerical final answer is recomputed from the question's own numbers by a calculator check that runs before each release; proofs and explanations were read, not machine-checked. The NCERT textbook is the authority — if something here disagrees with it, follow the book.
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Ex 7.2 Q1
A sample of 30 sweets from a big bag: 10 red, 8 green, 7 yellow, 5 blue. (i) Probability that a sweet picked from the sample is green. (ii) The bag has 600 sweets: estimate how many are yellow.
- (i) Total number of sweets in the sample is 30.
- (i) Number of green sweets in the sample is 8.
- (i) Probability of picking a green sweet = Number of green sweets / Total sweets = 8/30.
why?
Probability of an event = number of outcomes in its favour ÷ total number of equally likely outcomes. It is always from 0 (impossible) to 1 (certain).
- (i) Simplifying the fraction gives 4/15.
why?
Simplifying (combining like terms, cancelling common factors) changes how the expression looks, not its value, so the next step is easier.
- (ii) Total sweets in the big bag is 600.
- (ii) Number of yellow sweets in the sample is 7.
- (ii) Probability of picking a yellow sweet = 7/30.
why?
Probability of an event = number of outcomes in its favour ÷ total number of equally likely outcomes. It is always from 0 (impossible) to 1 (certain).
- (ii) Estimated number of yellow sweets in the bag = (7/30) × 600.
- (ii) Calculating the value gives 140.
Answer: (i) 4/15; (ii) 140
Ex 7.2 Q2
A sample of 40 students names a favourite club: Science 14, Arts 11, Sports 9, Debate 6; the school has 800 students. (i) Probability that a student from the sample prefers Arts. (ii) Estimate how many students in the school prefer Sports.
- (i) Total number of students in the sample is 40.
- (i) Number of students who prefer Arts is 11.
- (i) Probability = (Number of students preferring Arts) ÷ (Total number of students in sample).
why?
Probability of an event = number of outcomes in its favour ÷ total number of equally likely outcomes. It is always from 0 (impossible) to 1 (certain).
- (i) Probability = 11 ÷ 40 = 11/40.
why?
Probability of an event = number of outcomes in its favour ÷ total number of equally likely outcomes. It is always from 0 (impossible) to 1 (certain).
- (ii) Number of students in the sample who prefer Sports is 9.
- (ii) Probability that a student prefers Sports = 9 ÷ 40.
why?
Probability of an event = number of outcomes in its favour ÷ total number of equally likely outcomes. It is always from 0 (impossible) to 1 (certain).
- (ii) Total number of students in the school is 800.
- (ii) Estimated number of students preferring Sports = (Probability of preferring Sports) × (Total students in school).
why?
Probability of an event = number of outcomes in its favour ÷ total number of equally likely outcomes. It is always from 0 (impossible) to 1 (certain).
- (ii) Estimated number = (9/40) × 800.
- (ii) Estimated number = 9 × 20 = 180.
Answer: (i) 11/40; (ii) 180
Ex 7.2 Q3
Toss a coin 20 times and record heads/tails: (i) number of heads, (ii) number of tails, (iii) experimental probability of heads, (iv) probability of tails on one more toss.
- This is an experiment, so your counts will be your own. One example record of 20 tosses is shown here; other results are just as correct.
- (i) Suppose the 20 tosses gave 11 heads.
- (ii) Then the number of tails is 20 − 11 = 9.
- (iii) Experimental probability of heads = number of heads ÷ number of tosses = 11/20 = 0.55 (with your own count h of heads it is h/20).
why?
Experimental probability = number of times the event happened ÷ total number of trials; with more trials it tends to come closer to the theoretical probability.
- (iv) The next toss does not depend on the earlier ones. A fair coin has 2 equally likely outcomes and 1 of them is tails, so P(tails) = 1/2.
why?
Probability of an event = number of outcomes in its favour ÷ total number of equally likely outcomes. It is always from 0 (impossible) to 1 (certain).
Answer: (i) 11 and (ii) 9 in this example record (yours may differ); (iii) 11/20 = 0.55 here, in general heads ÷ 20; (iv) 1/2
Ex 7.2 Q4
Toss a paper cup 100 times and record whether it lands on its bottom, its top or its side (Fig. 7.5). Give each outcome its experimental probability.
- The counts come from your own 100 tosses, so answers differ. As one example record: bottom 30 times, top 20 times, side 50 times.
- The total number of trials is 100.
- The experimental probability of an event is calculated as the number of times the event occurs divided by the total number of trials.
why?
Experimental probability = number of times the event happened ÷ total number of trials; with more trials it tends to come closer to the theoretical probability.
- For the outcome 'bottom', the probability is 30 divided by 100, which simplifies to 0.3.
why?
Probability of an event = number of outcomes in its favour ÷ total number of equally likely outcomes. It is always from 0 (impossible) to 1 (certain).
- For the outcome 'top', the probability is 20 divided by 100, which simplifies to 0.2.
why?
Probability of an event = number of outcomes in its favour ÷ total number of equally likely outcomes. It is always from 0 (impossible) to 1 (certain).
- For the outcome 'side', the probability is 50 divided by 100, which simplifies to 0.5.
why?
Probability of an event = number of outcomes in its favour ÷ total number of equally likely outcomes. It is always from 0 (impossible) to 1 (certain).
- With your own counts b, t and s (b + t + s = 100), the probabilities are b/100, t/100 and s/100, and they add up to 1.
Answer: In this example record: P(bottom) = 0.3, P(top) = 0.2, P(side) = 0.5; with your own counts use (number of landings) ÷ 100.
Ex 7.2 Q5
Probability of an even number on one roll of a fair six-sided die.
- A fair six-sided die has 6 possible outcomes: 1, 2, 3, 4, 5, 6.
- The total number of possible outcomes is 6.
- The even numbers on the die are 2, 4, and 6.
- The number of favorable outcomes (even numbers) is 3.
- Probability is calculated as the number of favorable outcomes divided by the total number of outcomes.
why?
Probability of an event = number of outcomes in its favour ÷ total number of equally likely outcomes. It is always from 0 (impossible) to 1 (certain).
- Probability = 3 ÷ 6.
why?
Probability of an event = number of outcomes in its favour ÷ total number of equally likely outcomes. It is always from 0 (impossible) to 1 (certain).
- Simplifying the fraction gives 1/2.
why?
Simplifying (combining like terms, cancelling common factors) changes how the expression looks, not its value, so the next step is easier.
Answer: 1/2
Ex 7.2 Q6
A die rolled 12 times shows 3 three times. (i) Experimental probability of a 3; (ii) theoretical probability of a 3; (iii) why can they differ, and what happens with 60, 600 or 6000 rolls?
- (i) The die was rolled a total of 12 times.
- (i) The number 3 appeared 3 times in these rolls.
- (i) Experimental probability is the ratio of the number of times the event occurred to the total number of trials.
why?
Experimental probability = number of times the event happened ÷ total number of trials; with more trials it tends to come closer to the theoretical probability.
- (i) Experimental probability of getting a 3 = 3 ÷ 12 = 1/4.
why?
Experimental probability = number of times the event happened ÷ total number of trials; with more trials it tends to come closer to the theoretical probability.
- (ii) A standard die has 6 faces numbered 1 to 6.
- (ii) There is only one face with the number 3.
- (ii) Theoretical probability is the ratio of favorable outcomes to total possible outcomes.
why?
Probability of an event = number of outcomes in its favour ÷ total number of equally likely outcomes. It is always from 0 (impossible) to 1 (certain).
- (ii) Theoretical probability of getting a 3 = 1 ÷ 6 = 1/6.
why?
Probability of an event = number of outcomes in its favour ÷ total number of equally likely outcomes. It is always from 0 (impossible) to 1 (certain).
- (iii) The experimental probability differs from the theoretical probability because the number of trials (12) is small.
why?
Experimental probability = number of times the event happened ÷ total number of trials; with more trials it tends to come closer to the theoretical probability.
- (iii) With a small number of trials, random variation causes the observed frequency to deviate from the expected value.
- (iii) As the number of rolls increases to 60, 600, or 6000, the experimental probability gets closer to the theoretical probability of 1/6.
why?
Experimental probability = number of times the event happened ÷ total number of trials; with more trials it tends to come closer to the theoretical probability.
Answer: (i) 1/4; (ii) 1/6; (iii) They differ due to the small number of trials, and the experimental probability approaches the theoretical probability as the number of trials increases.
Other exercises in this chapter
- Exercise Set 7.1 — 1 questions
- Exercise Set 7.3 — 3 questions
- Exercise Set 7.4 — 2 questions
- End-of-chapter exercises — 16 questions
← The Mathematics of Maybe: Introduction to Probability: notes, practice and all exercises
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