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Class 9 Ganita ManjariClass 9 Maths Solutions | 2026–27
Chapter 7: The Mathematics of Maybe: Introduction to ProbabilityPage 165 – 166All 6 Questions on This Page

Class 9 Maths Chapter 7 Exercise Set 7.2 Solutions

Complete step-by-step solutions for Class 9 Mathematics Ganita Manjari Chapter 7 Exercise Set 7.2: Measuring Probability Objectively (Page 165–166). Covers experimental vs theoretical probability, sample surveys, coin and die experiments, and the Law of Large Numbers.

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Key Concepts for Exercise Set 7.2

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1

Experimental Probability

Experimental probability is based on the results of actual trials or observations.

Experimental Probability = Number of times event occurred / Total trials
2

Theoretical Probability

When all possible outcomes are equally likely, theoretical probability is the ratio of favourable outcomes to total possible outcomes.

Theoretical Probability = Number of favourable outcomes / Number of possible outcomes
3

Sample and Population

A sample is a smaller group selected from a larger population to collect information and estimate probabilities or characteristics of the population.

4

Relative Frequency

Relative frequency is the number of times an event occurs divided by the total number of observations or trials.

Question 1
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A teacher mixes a large bag of sweets of different colours and randomly selects a sample of 30 sweets. She counts the number of sweets of each colour: 10 red sweets | 8 green sweets | 7 yellow sweets | 5 blue sweets (i) Calculate the probability that a randomly picked sweet from the sample is green. (ii) If there are 600 sweets in total in the large bag, estimate how many are likely to be yellow, based on the sample results.

Solution
Given:
Total number of sweets in the sample = 30
Number of red sweets = 10
Number of green sweets = 8
Number of yellow sweets = 7
Number of blue sweets = 5
We know,

P(E) = Number of favourable outcomes / Total number of outcomes

(i) Probability that a randomly picked sweet is green:
Number of green sweets = 8

P(Green) = Number of green sweets / Total number of sweets in sample

= 830
= 415
Therefore,
P(Green) = 415
(ii) Estimate of yellow sweets in the large bag:

Number of yellow sweets in the sample = 7

P(Yellow) = Number of yellow sweets in sample / Total number of sweets in sample

= 730
Total number of sweets in the large bag = 600

Estimated number of yellow sweets = P(Yellow) × Total sweets in the bag

= 730 × 600
= 7 × 20
= 140
Therefore,

140 sweets are likely to be yellow.

Answer:(i) P(Green) = 415 | (ii) 140 sweets are likely to be yellow
Question 2
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A survey is conducted at a school where a random sample of 40 students is asked about their favourite club. The responses are: 14 students: Science Club | 11 students: Arts Club | 9 students: Sports Club | 6 students: Debate Club Assume there are 800 students in the whole school. (i) What is the probability that a randomly chosen student from the sample prefers the Arts Club? (ii) Using the sample results, estimate how many students in the whole school are likely to prefer the Sports Club.

Solution
Given:
Total number of students surveyed in the sample = 40

Number of students preferring Science Club = 14

Number of students preferring Arts Club = 11

Number of students preferring Sports Club = 9

Number of students preferring Debate Club = 6

Total number of students in the whole school = 800
We know,

P(E) = Number of favourable outcomes / Total number of outcomes

(i) Probability that a student prefers the Arts Club:

Number of students preferring the Arts Club = 11

P(Arts Club) = Number of students preferring Arts Club / Total students in sample

= 1140
Therefore,
P(Arts Club) = 1140
(ii) Estimate of students in the whole school preferring the Sports Club:

Number of students preferring the Sports Club in the sample = 9

P(Sports Club) = Number of students preferring Sports Club in sample / Total students in sample

= 940

Estimated number of students in school = P(Sports Club) × Total students in school

= 940 × 800
= 9 × 20
= 180
Therefore,

180 students in the whole school are likely to prefer the Sports Club.

Answer:(i) P(Arts Club) = 1140 | (ii) 180 students in the whole school are likely to prefer the Sports Club
Question 3
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Toss a coin 20 times and record the result each time (heads or tails). (i) How many times did you get heads? (ii) How many times did you get tails? (iii) Calculate the experimental probability of getting heads. (iv) If you toss the coin once more, what is the probability of getting tails?

Solution

This is an activity-based question, so the actual numbers of heads and tails will depend on the results of the 20 tosses.

For one possible record of 20 tosses:

H, T, H, H, T, T, H, T, H, H,

T, H, T, T, H, H, T, H, T, H

Total number of tosses = 20
(i) Number of times heads appeared:

Counting the results,

Number of Heads = 11
Therefore,

11 heads were obtained.

(ii) Number of times tails appeared:

Since there were 20 tosses altogether,

Number of Tails = 20 − 11
= 9
Therefore,

9 tails were obtained.

(iii) Experimental probability of getting heads:
We know,

Experimental Probability = Number of times the event occurred / Total number of trials

Therefore,
P(Heads) = 1120
= 0.55
Hence,
P(Heads) = 1120 = 0.55
(iv) Probability of getting tails on the next toss:

For a fair coin, heads and tails are equally likely.

Therefore,
P(Tails) = 12
Hence,
P(Tails) = 12
Answer:(i) 11 heads (model record) | (ii) 9 tails (model record) | (iii) P(Heads) = 1120 = 0.55 | (iv) P(Tails) = 12
Question 4
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Toss a paper cup into the air 100 times. After each toss record whether the cup lands on its bottom, upside down on its top or on its side (See Fig. 7.5). Assign probabilities to the outcomes by using experimental probability.

Three Landing Positions of a Paper CupFig. 7.5
Illustration of a paper cup landing in three different ways: bottom, upside down on top, and on its side

Fig. 7.5: A paper cup can land on its bottom (upright), upside down on its top (rim), or on its side.

Solution

This is an activity-based experiment, so the results may be different for different students.

For example, suppose the cup is tossed 100 times and the following results are obtained:

Landing positionNumber of times
Bottom15
Top10
Side75
Total100
We know,

Experimental Probability = Number of times the outcome occurred / Total number of trials

(i) Probability of landing on its bottom:
P(Bottom) = 15100
= 320
Therefore,
P(Bottom) = 320
(ii) Probability of landing upside down on its top:
P(Top) = 10100
= 110
Therefore,
P(Top) = 110
(iii) Probability of landing on its side:
P(Side) = 75100
= 34
Therefore,
P(Side) = 34

Check:

320 + 110 + 34
= 320 + 220 + 1520
= 1
Hence, for this model experiment,
P(Bottom) = 320
P(Top) = 110
P(Side) = 34
Answer:Model experiment results: P(Bottom) = 320 | P(Top) = 110 | P(Side) = 34
Question 5
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What is the probability of getting an even number when rolling a fair 6-sided die?

Solution

A fair 6-sided die has the possible outcomes:

1, 2, 3, 4, 5, 6

The even numbers are:

2, 4, 6
So, the number of favourable outcomes is:
3

The total number of possible outcomes is:

6
We know,

P(E) = Number of favourable outcomes / Number of possible outcomes

Therefore,
P(Even number) = 36
= 12
Hence,
12

is the probability of getting an even number.

Answer:P(Even number) = 12
Question 6
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Suppose you roll a 6-sided die 12 times and get a ‘3’ three times. (i) What is the experimental probability of rolling a ‘3’? (ii) What is the theoretical probability of rolling a ‘3’? (iii) Why might these probabilities be different? What would you expect to happen if you roll the die 60, 600, or 6000 times?

Solution
(i) Experimental probability of rolling a 3:

The number of times a 3 was obtained is:

3

The total number of rolls is:

12
We know,

Experimental Probability = Number of times the event occurred / Total number of trials

Therefore,
P(3) = 312
= 14
Hence,
14

is the experimental probability of rolling a 3.

(ii) Theoretical probability of rolling a 3:

A fair 6-sided die has 6 equally likely outcomes:

1, 2, 3, 4, 5, 6

Only one outcome is favourable, namely 3.

Therefore,
P(3) = 16
Hence,
16

is the theoretical probability of rolling a 3.

(iii) Why might the probabilities be different?

The experimental probability is based on the results of a limited number of actual trials.

Here,

14 ≠ 16

because getting a 3 exactly 3 times in 12 rolls is only one possible experimental result.

If the die is rolled many more times, the experimental probability is expected to get closer to the theoretical probability:

16
So, with 60, 600, or 6000 rolls, the experimental probability would generally be expected to become closer to 1/6 as the number of trials increases.

This is the idea behind the Law of Large Numbers.

Answer:(i) Experimental: P(3) = 14 | (ii) Theoretical: P(3) = 16 | (iii) Expected to approach 16 as trials increase (Law of Large Numbers)

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