Class 9 Maths Ganita Manjari Chapter 7 Exercise 7.2 Solutions

Experimental probability is based on actual observations or trials, while theoretical probability is based on equally likely outcomes.
Class 9 Maths Ganita Manjari Chapter 7 Exercise 7.2 connects these ideas with sweets, surveys, coin tosses, cup tosses and die rolls.

Exercise 7.2 from Chapter 7, The Mathematics of Maybe: Introduction to Probability Class 9, moves from the probability scale to objective ways of measuring probability. Students use sample data, repeated trials, relative frequency and fair-outcome reasoning. Class 9 Maths Ganita Manjari Chapter 7 Exercise 7.2 Solutions cover six textbook questions on experimental probability Class 9, theoretical probability Class 9, survey-based estimates, coin toss data, paper cup trials and fair die probability Class 9. The chapter explains that experimental probability uses actual trial data, while theoretical probability uses favourable outcomes divided by possible outcomes in a fair situation.

Key Takeaways

• Experimental Probability: It is calculated from observed data or repeated trials.
• Relative Frequency: It is the fraction of times an event occurs in the total trials.
• Theoretical Probability: It assumes all possible outcomes are equally likely.
• Larger Trials: Experimental probability usually gets closer to theoretical probability as trials increase.

Class 9 Maths Ganita Manjari Chapter 7 Exercise 7.2 Solutions Structure 2026

Class 9 Maths Ganita Manjari Chapter 7 Exercise 7.2 Solutions for Sample Results

Exercise 7.2 begins with probability estimates based on samples. The main formula used is favourable observations divided by total observations.

Q1. 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.

Q1(i). Calculate the probability that a randomly picked sweet from the sample is green.

The probability of picking a green sweet from the sample is 4/15.

Given:

Total sweets in sample = 30

Green sweets = 8

Use:

Probability = Number of favourable outcomes / Total number of outcomes

Substitute values:

Probability of green sweet = 8/30

Probability of green sweet = 4/15

Decimal form:

4/15 = 0.2666...

Percentage form:

0.2666... = 26.67%

Answer:

The probability that a randomly picked sweet is green is 4/15, or about 26.67%.

Q1(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.

The estimated number of yellow sweets is 140.

Given:

Yellow sweets in sample = 7

Total sweets in sample = 30

Total sweets in large bag = 600

First find probability of yellow sweet:

Probability of yellow sweet = 7/30

Now estimate yellow sweets in the large bag:

Estimated yellow sweets = 7/30 × 600

Estimated yellow sweets = 7 × 20

Estimated yellow sweets = 140

Answer:

About 140 sweets are likely to be yellow.

Ganita Manjari Class 9 Chapter 7 Exercise 7.2: Probability from Survey Data

Survey data gives an estimate of probability using a sample. The estimate becomes useful when the sample is chosen randomly and represents the larger group.

Q2. 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.

Q2(i). What is the probability that a randomly chosen student from the sample prefers the Arts Club?

The probability that a student prefers the Arts Club is 11/40.

Given:

Total students in sample = 40

Students who prefer Arts Club = 11

Use:

Probability = Number of favourable outcomes / Total number of outcomes

Substitute values:

Probability of Arts Club = 11/40

Decimal form:

11/40 = 0.275

Percentage form:

0.275 = 27.5%

Answer:

The probability that a randomly chosen student from the sample prefers the Arts Club is 11/40, or 27.5%.

Q2(ii). Using the sample results, estimate how many students in the whole school are likely to prefer the Sports Club.

The estimated number of students who prefer the Sports Club is 180.

Given:

Students who prefer Sports Club in sample = 9

Total students in sample = 40

Total students in school = 800

First find probability of Sports Club:

Probability of Sports Club = 9/40

Now estimate for 800 students:

Estimated Sports Club students = 9/40 × 800

Estimated Sports Club students = 9 × 20

Estimated Sports Club students = 180

Answer:

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

Class 9 Maths Chapter 7 Exercise 7.2 Solutions for Coin Toss Experiment

A coin toss experiment gives experimental probability from actual results. Each student’s answer may vary because the result depends on the 20 tosses recorded.

Q3. Toss a coin 20 times and record the result each time.

Q3(i). How many times did you get heads?

The number of heads depends on the actual 20 tosses.

Example record:

Heads = 11

Answer:

In one possible experiment, heads came 11 times.

Q3(ii). How many times did you get tails?

The number of tails depends on the same 20 tosses.

Example record:

Tails = 9

Check:

Heads + Tails = 20

11 + 9 = 20

Answer:

In one possible experiment, tails came 9 times.

Q3(iii). Calculate the experimental probability of getting heads.

Using the example record, the experimental probability of getting heads is 11/20.

Use:

Experimental probability = Number of times event occurred / Total number of trials

Substitute values:

Experimental probability of heads = 11/20

Decimal form:

11/20 = 0.55

Percentage form:

0.55 = 55%

Answer:

Using this sample result, the experimental probability of getting heads is 11/20, or 55%.

Q3(iv). If you toss the coin once more, what is the probability of getting tails?

The probability of getting tails in the next toss is 1/2 for a fair coin.

Reason:

A fair coin has two equally likely outcomes.

Sample space:

S = {H, T}

Favourable outcome for tails:

T

So:

Probability of tails = 1/2

Answer:

The probability of getting tails in the next toss is 1/2.

Class 9 Maths Ganita Manjari Chapter 7 Solutions for Paper Cup Experiment

A paper cup toss has three possible landing types: bottom, top and side. The experimental probabilities are calculated from the observed counts in 100 tosses.

Q4. 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. Assign probabilities to the outcomes by using experimental probability.

The probabilities depend on the actual 100 recorded tosses.

Use:

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

Total trials:

100

Example observation table:

Check:

24 + 18 + 58 = 100

So:

Probability of bottom = 24/100

Probability of bottom = 0.24

Probability of top = 18/100

Probability of top = 0.18

Probability of side = 58/100

Probability of side = 0.58

Answer:

Using the example data, the probabilities are 0.24 for bottom, 0.18 for top and 0.58 for side.

The Mathematics of Maybe Introduction to Probability Class 9: Fair Die Probability

A fair 6-sided die has six equally likely outcomes. The sample space is {1, 2, 3, 4, 5, 6}.

Q5. What is the probability of getting an even number when rolling a fair 6-sided die?

The probability of getting an even number is 1/2.

Sample space:

S = {1, 2, 3, 4, 5, 6}

Total possible outcomes:

6

Even numbers:

2, 4, 6

Number of favourable outcomes:

3

Use:

Probability = Number of favourable outcomes / Number of possible outcomes

Substitute values:

Probability of even number = 3/6

Probability of even number = 1/2

Answer:

The probability of getting an even number is 1/2.

Class 9 Maths Probability Solutions: Experimental and Theoretical Probability

Exercise 7.2 ends by comparing experimental probability with theoretical probability. Experimental probability comes from actual rolls, while theoretical probability comes from equally likely outcomes.

Q6. Suppose you roll a 6-sided die 12 times and get a ‘3’ three times.

Q6(i). What is the experimental probability of rolling a ‘3’?

The experimental probability of rolling a 3 is 1/4.

Given:

Total rolls = 12

Number of times 3 occurred = 3

Use:

Experimental probability = Number of times event occurred / Total number of trials

Substitute values:

Experimental probability of rolling 3 = 3/12

Experimental probability of rolling 3 = 1/4

Decimal form:

1/4 = 0.25

Percentage form:

0.25 = 25%

Answer:

The experimental probability of rolling a 3 is 1/4, or 25%.

Q6(ii). What is the theoretical probability of rolling a ‘3’?

The theoretical probability of rolling a 3 is 1/6.

For a fair 6-sided die:

Sample space:

S = {1, 2, 3, 4, 5, 6}

Total possible outcomes:

6

Favourable outcome:

3

Number of favourable outcomes:

1

So:

Theoretical probability of rolling 3 = 1/6

Decimal form:

1/6 = 0.1666...

Percentage form:

0.1666... = 16.67%

Answer:

The theoretical probability of rolling a 3 is 1/6, or about 16.67%.

Q6(iii). Why might these probabilities be different? What would you expect to happen if you roll the die 60, 600, or 6000 times?

These probabilities may be different because experimental probability depends on actual results from a small number of trials.

In 12 rolls, getting 3 three times gives:

Experimental probability = 1/4

The fair-die theoretical probability is:

Theoretical probability = 1/6

With more trials, the experimental probability is expected to get closer to 1/6.

Expected pattern:

For 60 rolls:

Experimental probability may move closer to 1/6.

For 600 rolls:

Experimental probability should be much closer to 1/6.

For 6000 rolls:

Experimental probability should be very close to 1/6.

Answer:

The difference occurs because 12 rolls are a small sample. As the number of rolls increases, the experimental probability is expected to approach the theoretical probability of 1/6.

Measuring Probability Objectively: Concepts Used in Exercise 7.2

Exercise 7.2 uses two objective ways to estimate probability: collecting evidence from trials or data, and using theoretical reasoning with equally likely outcomes. The textbook introduces these as experimental probability and theoretical probability.

Experimental Probability Class 9

Experimental probability is calculated from actual results.

Copy-friendly formula:

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

Example:

A die is rolled 12 times.

A 3 appears 3 times.

Experimental probability of 3 = 3/12

Experimental probability of 3 = 1/4

Relative Frequency Class 9

Relative frequency tells how often an event occurs compared to the total number of observations.

Copy-friendly formula:

Relative frequency = Frequency of event / Total frequency

Example:

Green sweets = 8

Total sweets = 30

Relative frequency of green = 8/30

Relative frequency of green = 4/15

Theoretical Probability Class 9

Theoretical probability is used when all outcomes are equally likely.

Copy-friendly formula:

Theoretical probability = Number of favourable outcomes / Number of possible outcomes

Example:

Even numbers on a die = {2, 4, 6}

Total die outcomes = 6

Probability of even number = 3/6

Probability of even number = 1/2

Probability from Survey Data

Survey-based probability uses a sample to estimate a larger group.

Copy-friendly formula:

Estimated number = Sample probability × Total population

Example:

Sports Club probability = 9/40

Total students = 800

Estimated Sports Club students = 9/40 × 800

Estimated Sports Club students = 180

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