Important Questions for Class 9 Maths (Ganita Manjari I) Chapter 7 The Mathematics of Maybe: Introduction to Probability - 2026-27

The important questions for Class 9 Maths Chapter 7 help students apply probability concepts to real-life situations, understand the chances of different outcomes and solve problems with confidence. Practising these questions with solutions helps improve logical thinking and accuracy.

For more practice across subjects, explore Class 9 Important Questions.

Class 9 Maths Chapter 7 Important Questions - MCQs

Q1. A weather report states that the probability of rain tomorrow is 0.8. What does this probability indicate?

(a) It will definitely rain tomorrow.

(b) There is an 80% chance of rain tomorrow.

(c) It will rain for exactly 8 hours.

(d) Rainfall is impossible tomorrow.

Answer: (b) There is an 80% chance of rain tomorrow.

Explanation: A probability of 0.8 represents an 80% chance of an event occurring. It means rain is more likely than not, but it is not certain.

Q2. A student rolls a fair six-sided die. Which of the following events is impossible?

(a) Getting an even number

(b) Getting a number less than 4

(c) Getting a number greater than 6

(d) Getting an odd number

Answer: (c) Getting a number greater than 6

Explanation: A standard six-sided die has numbers 1, 2, 3, 4, 5 and 6. Therefore, getting a number greater than 6 is impossible, and its probability is 0.

Q3. A fair coin is tossed 80 times, and heads appears 36 times. What is the experimental probability of getting heads?

(a) 0.25

(b) 0.45

(c) 0.50

(d) 0.80

Answer: (b) 0.45

Explanation:

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

$$P(H)=\dfrac{36}{80}$$

$$P(H)=\dfrac{9}{20}=0.45$$

Therefore, the experimental probability of getting heads is 0.45 or 45%.

Q4. Two fair coins are tossed simultaneously. What is the probability of getting exactly one head?

(a) $$\dfrac{1}{4}$$

(b) $$\dfrac{1}{2}$$

(c) $$\dfrac{3}{4}$$

(d) 1

Answer: (b) $$\dfrac{1}{2}$$

Explanation:

Sample space:

S = {HH, HT, TH, TT}

Total possible outcomes = 4

Favourable outcomes = {HT, TH}

Number of favourable outcomes = 2

$$P(\text{Exactly one head})=\dfrac{2}{4}=\dfrac{1}{2}$$

Final Answer: $$\dfrac{1}{2}$$

Class 9 Maths Chapter 7 Very Short Answer Questions

Q5. What is a random experiment? Give one example and explain why its outcome cannot be predicted with certainty.

Answer:

A random experiment is an experiment whose possible outcomes are known, but the exact outcome cannot be predicted in advance.

For example, when a fair coin is tossed, it can show heads or tails. However, we cannot know which side will appear before tossing it.

Q6. A box contains 4 red balls, 3 blue balls and 5 yellow balls. One ball is selected randomly. Find the probability of selecting a blue ball.

Solution:

Total number of balls = 4 + 3 + 5 = 12

Number of blue balls = 3

Probability = Number of favourable outcomes / Total number of possible outcomes

$$P(\text{Blue})=\dfrac{3}{12}$$

$$P(\text{Blue})=\dfrac{1}{4}$$

Final Answer: The probability of selecting a blue ball is $$\dfrac{1}{4}$$.

Q7. What is the difference between experimental probability and theoretical probability?

Answer:

Experimental probability is calculated using the results obtained from actual trials or observations.

Theoretical probability is calculated by considering all possible outcomes when they are equally likely.

For example, the theoretical probability of getting heads when tossing a fair coin is $$\dfrac{1}{2}$$, but the experimental probability may be different when the coin is tossed a small number of times.

Class 9 Maths Chapter 7 Short Answer Questions

Q8. A spinner is divided into 8 equal sections numbered 1 to 8. It is spun once. Find the probability of getting (i) a multiple of 2, (ii) a prime number, and (iii) a number greater than 5.

Solution:

The spinner has 8 equally likely outcomes.

Sample space:

S = {1, 2, 3, 4, 5, 6, 7, 8}

Total possible outcomes = 8

(i) Probability of getting a multiple of 2

Favourable outcomes = {2, 4, 6, 8}

Number of favourable outcomes = 4

$$P(\text{Multiple of 2})=\dfrac{4}{8}=\dfrac{1}{2}$$

(ii) Probability of getting a prime number

Prime numbers = {2, 3, 5, 7}

Number of favourable outcomes = 4

$$P(\text{Prime number})=\dfrac{4}{8}=\dfrac{1}{2}$$

(iii) Probability of getting a number greater than 5

Favourable outcomes = {6, 7, 8}

Number of favourable outcomes = 3

$$P(\text{Number greater than 5})=\dfrac{3}{8}$$

Final Answer:

(i) $$\dfrac{1}{2}$$

(ii) $$\dfrac{1}{2}$$

(iii) $$\dfrac{3}{8}$$

Q9. A student tosses a fair coin five times and gets heads in every toss. The student believes that the next toss must result in tails. Is the student correct? Explain using the concept of independent events.

Answer:

No, the student is incorrect.

Each toss of a fair coin is an independent event. This means the result of one toss does not affect the result of another toss.

The probability of getting tails on the next toss remains:

$$P(T)=\dfrac{1}{2}$$

Similarly, the probability of getting heads is:

$$P(H)=\dfrac{1}{2}$$

The belief that tails must appear because heads occurred repeatedly is called the Gambler's Fallacy.

Final Answer: The probability of getting tails on the next toss is still $$\dfrac{1}{2}$$ or 50%.

Q10. A school records the mode of transport used by 120 students. The results show that 48 students travel by bus, 36 walk, 24 use bicycles and 12 travel by car. If one student is selected randomly, find the estimated probability that the student (i) travels by bus, (ii) walks or cycles, and (iii) travels by car.

Solution:

Total students = 120

(i) Probability of travelling by bus

Number of students travelling by bus = 48

$$P(\text{Bus})=\dfrac{48}{120}=\dfrac{2}{5}$$

(ii) Probability of walking or cycling

Students who walk = 36

Students who cycle = 24

Total = 36 + 24 = 60

$$P(\text{Walking or cycling})=\dfrac{60}{120}=\dfrac{1}{2}$$

(iii) Probability of travelling by car

Students travelling by car = 12

$$P(\text{Car})=\dfrac{12}{120}=\dfrac{1}{10}$$

Final Answer:

(i) $$\dfrac{2}{5}$$

(ii) $$\dfrac{1}{2}$$

(iii) $$\dfrac{1}{10}$$

These probabilities are based on the observed transport data.

Class 9 Maths Chapter 7 Long Answer Questions

Q11. A bag contains 5 red balls, 4 green balls and 3 yellow balls. Two balls are drawn one after another without replacement. Find the probability that (i) both balls are red, (ii) the first ball is green and the second is yellow, and (iii) both balls are of different colours.

Solution:

Given:

Red balls = 5

Green balls = 4

Yellow balls = 3

Total balls = 12

Since the balls are drawn without replacement, the total number of balls decreases after the first draw.

(i) Probability that both balls are red

Probability of first red ball:

$$P(R_1)=\dfrac{5}{12}$$

After drawing one red ball:

Remaining red balls = 4

Remaining total balls = 11

Probability of second red ball:

$$P(R_2\mid R_1)=\dfrac{4}{11}$$

Therefore:

$$P(\text{Both red})=\dfrac{5}{12}\times\dfrac{4}{11}$$

$$=\dfrac{20}{132}=\dfrac{5}{33}$$

(ii) Probability that the first ball is green and the second is yellow

Probability of first green ball:

$$P(G_1)=\dfrac{4}{12}$$

After drawing one green ball, 11 balls remain, including 3 yellow balls.

Probability of second yellow ball:

$$P(Y_2\mid G_1)=\dfrac{3}{11}$$

Therefore:

$$P(\text{Green then yellow})=\dfrac{4}{12}\times\dfrac{3}{11}$$

$$=\dfrac{12}{132}=\dfrac{1}{11}$$

(iii) Probability that both balls are of different colours

First, calculate the probability that both balls have the same colour.

Both red:

$$P(RR)=\dfrac{5}{12}\times\dfrac{4}{11}=\dfrac{20}{132}$$

Both green:

$$P(GG)=\dfrac{4}{12}\times\dfrac{3}{11}=\dfrac{12}{132}$$

Both yellow:

$$P(YY)=\dfrac{3}{12}\times\dfrac{2}{11}=\dfrac{6}{132}$$

Probability of the same colour:

$$P(\text{Same colour})=\dfrac{20+12+6}{132}$$

$$=\dfrac{38}{132}=\dfrac{19}{66}$$

Probability of different colours:

$$P(\text{Different colours})=1-\dfrac{19}{66}$$

$$=\dfrac{47}{66}$$

Final Answer:

(i) Both red = $$\dfrac{5}{33}$$

(ii) Green followed by yellow = $$\dfrac{1}{11}$$

(iii) Different colours = $$\dfrac{47}{66}$$

Q12. A fair coin is tossed three times. Construct a tree diagram or systematically list all possible outcomes. Find the probability of (i) getting exactly two heads, (ii) getting at least two tails, and (iii) getting the same result in all three tosses.

Solution:

Step 1: List the sample space.

When a fair coin is tossed three times, each toss has two possible outcomes: H or T.

Total possible outcomes:

$$2\times2\times2=8$$

Sample space:

S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

All eight outcomes are equally likely.

Step 2: Find the probability of exactly two heads.

Favourable outcomes:

{HHT, HTH, THH}

Number of favourable outcomes = 3

$$P(\text{Exactly two heads})=\dfrac{3}{8}$$

Step 3: Find the probability of at least two tails.

At least two tails means getting two tails or three tails.

Favourable outcomes:

{HTT, THT, TTH, TTT}

Number of favourable outcomes = 4

$$P(\text{At least two tails})=\dfrac{4}{8}=\dfrac{1}{2}$$

Step 4: Find the probability of the same result in all three tosses.

Favourable outcomes:

{HHH, TTT}

Number of favourable outcomes = 2

$$P(\text{Same result})=\dfrac{2}{8}=\dfrac{1}{4}$$

Final Answer:

(i) Exactly two heads = $$\dfrac{3}{8}$$

(ii) At least two tails = $$\dfrac{1}{2}$$

(iii) Same result in all three tosses = $$\dfrac{1}{4}$$

Q13. A school conducts a survey of 200 randomly selected students to understand their preferred extracurricular activities. The results are given below. Use the data to calculate probabilities and estimate preferences for the entire school of 1,500 students.

Find:

(i) The estimated probability that a randomly selected student prefers Sports.

(ii) The estimated probability that a student prefers Music or Art.

(iii) The estimated number of students who prefer Dance in the entire school.

(iv) Explain why the estimate may not exactly match the actual preferences of all 1,500 students.

Solution:

Step 1: Find the probability of preferring Sports.

Number of students preferring Sports = 80

Total surveyed students = 200

$$P(\text{Sports})=\dfrac{80}{200}$$

$$P(\text{Sports})=\dfrac{2}{5}=0.4$$

Therefore, the estimated probability is 40%.

Step 2: Find the probability of preferring Music or Art.

Students preferring Music = 50

Students preferring Art = 40

Total favourable responses = 50 + 40 = 90

$$P(\text{Music or Art})=\dfrac{90}{200}$$

$$=\dfrac{9}{20}=0.45$$

Therefore, the estimated probability is 45%.

Step 3: Estimate the number of students who prefer Dance.

Students preferring Dance in the sample = 30

Sample size = 200

Estimated probability of preferring Dance:

$$P(\text{Dance})=\dfrac{30}{200}=0.15$$

Total school population = 1,500

Estimated number of students:

$$=0.15\times1500$$

= 225 students

Step 4: Explain why the estimate may differ from the actual number.

The survey includes only 200 students out of 1,500.

The estimate assumes that the selected sample represents the preferences of the entire school.

If the sample does not represent students from different classes and groups fairly, the estimate may be inaccurate.

A larger, well-selected sample can help improve the reliability of the estimate.

Final Answer:

(i) Probability of Sports = 0.4 or 40%

(ii) Probability of Music or Art = 0.45 or 45%

(iii) Estimated students preferring Dance = 225

(iv) The estimate may differ because it is based on a sample rather than the entire school population.

Tips to Solve Class 9 Maths Chapter 7 Important Questions Easily

Understanding probability concepts makes solving questions easier and improves accuracy. Students can follow these tips to prepare for exams:

• Identify Outcomes: List all possible outcomes before calculating probability.

• Understand Events: Learn about certain, impossible and equally likely events.

• Use Examples: Practise probability problems involving coins, dice and everyday situations.

• Remember the Range: Probability always lies between 0 and 1.

• Check Answers: Review calculations and correct mistakes to improve accuracy.

Benefits of Vedantu's Class 9 Maths Chapter 7 Important Questions PDF

Vedantu's Class 9 Maths Chapter 7 Important Questions PDF helps students practise probability with clear answers and organised learning resources.

• Important Questions: Access chapter-focused problems for exam preparation.

• Step-by-Step Solutions: Understand how to solve questions correctly.

• Downloadable PDF: Practise anytime, even without internet access.

• Self-Assessment: Check answers and identify areas for improvement.

• Exam Preparation: Build confidence through regular practice. Download Vedantu's Important Questions with Answers PDF to strengthen your preparation for the 2026-27 exams.

Important Study Materials for Class 9 Maths Chapter 7 The Mathematics of Maybe: Introduction to Probability

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