Important Questions Class 9 Maths Chapter 7 Introduction to Probability 2026-2027

Probability measures how likely an event is to happen. It uses numbers from 0 to 1, where 0 means impossible and 1 means certain.

Important questions class 9 maths chapter 7 help students practise probability scale, randomness, experimental probability, theoretical probability, sample space, events and tree diagrams. This chapter connects maths with daily-life situations like coin tosses, dice rolls, surveys, games and weather predictions.

Class 9 Maths Chapter 7 begins with questions that do not have fixed answers: Will it rain today? Will a team win a match? Will a student get selected in a lucky draw? These situations involve chance, uncertainty and randomness.

The chapter teaches students how to measure this uncertainty using probability. Students learn how to list possible outcomes, identify favourable outcomes, calculate probability from experiments, compare it with theoretical probability and use tree diagrams for multi-step experiments. 

Key Takeaways from Class 9 Maths Chapter 7

Important Questions Class 9 Maths Chapter 7 with Answers

These questions cover the basic concepts. Students should define each term clearly before solving numerical problems.

Important Questions Class 9 Maths Chapter 7: Basic Concepts

Q1. What is probability?

Probability is a measure of how likely an event is to occur.

It is written as a number between 0 and 1. A probability of 0 means the event is impossible. A probability of 1 means the event is certain.

Q2. What is a random experiment?

A random experiment is an action that can be repeated, but its exact outcome cannot be predicted in advance.

Tossing a coin and rolling a die are random experiments. The possible outcomes are known, but the exact result is uncertain.

Q3. What is the probability scale?

The probability scale shows likelihood from 0 to 1.

0 means impossible. 0.5 means equally likely. 1 means certain. Values between 0 and 1 show different levels of chance.

Q4. What is an impossible event?

An impossible event is an event that cannot happen.

For example, getting a number greater than 6 on a standard die is impossible. Its probability is 0.

Q5. What is a certain event?

A certain event is an event that will definitely happen.

For example, getting a number from 1 to 6 when rolling a standard die is certain. Its probability is 1.

Probability Class 9 Important Questions on Probability Scale

The probability scale class 9 questions help students compare events before using formulas. These questions test reasoning more than calculation.

Q1. Classify this event: The next Monday will come after Sunday.

This event is certain.

In the calendar order, Monday always comes after Sunday. So, its probability is 1.

Q2. Classify this event: It will snow in Mumbai in July.

This event is impossible or extremely unlikely.

Mumbai has a tropical coastal climate and does not experience snowfall in July. For school-level probability scale questions, students can mark it near 0.

Q3. Classify this event: Tossing a fair coin and getting heads.

This event has an even chance.

A fair coin has two equally likely outcomes: heads and tails.

P({Heads}) = (1)/(2)

Q4. Classify this event: Rolling a 3 on a fair die.

This event is possible but less likely than not getting 3.

A die has six equally likely outcomes. Only one outcome is 3.

P(3) = (1)/(6)

Q5. Classify this event: Choosing a red sweet from a bag of all red sweets.

This event is certain.

Every sweet in the bag is red. So, the probability is 1.

Experimental Probability Class 9 Question Answer

Experimental probability class 9 questions use actual trials or collected data. Students should write both the event count and the total trials clearly.

Experimental Probability Class 9 Formula Questions

Q1. What is experimental probability?

Experimental probability is probability based on observations, trials or collected data.

{Experimental Probability} = frac{{Number of times the event occurred}}{{Total number of trials}}

Q2. A die is rolled 50 times and lands on 4 exactly 8 times. Find the experimental probability of rolling 4.

Number of times 4 occurred = 8.

Total trials = 50.

P(4) = (8)/(50)

= (4)/(25)

= 0.16

So, the experimental probability is 0.16 or 16%.

Q3. A coin is tossed 20 times. Heads appears 11 times. Find the experimental probability of heads.

Number of heads = 11.

Total tosses = 20.

P({Heads}) = (11)/(20)

= 0.55

So, the experimental probability of heads is 0.55.

Q4. In a class of 50 students, 20 students like mango. Find the probability that a randomly chosen student likes mango.

Number of students who like mango = 20.

Total students = 50.

P({Mango}) = (20)/(50)

= (2)/(5)

= 0.4

So, the probability is 0.4 or 40%.

Q5. A sample of 30 sweets has 10 red, 8 green, 7 yellow and 5 blue sweets. Find the probability of picking a green sweet.

Number of green sweets = 8.

Total sweets = 30.

P({Green}) = (8)/(30)

= (4)/(15)

So, the probability is (4/15).

Theoretical Probability Class 9 Important Questions

Theoretical probability class 9 questions work when all outcomes are equally likely. Students should identify favourable outcomes first.

Q1. What is theoretical probability?

Theoretical probability is the expected probability in a fair situation where all outcomes are equally likely.

P(E) = frac{{Number of favourable outcomes}}{{Number of possible outcomes}}

Q2. What is the probability of getting an even number on a fair die?

Sample space:

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

Even numbers:

E = {2,4,6}

Number of favourable outcomes = 3.

Total outcomes = 6.

P({Even}) = (3)/(6)

= (1)/(2)

Q3. What is the probability of getting a number greater than 4 on a fair die?

Numbers greater than 4:

E = {5,6}

Total outcomes = 6.

P({Greater than 4}) = (2)/(6)

= (1)/(3)

Q4. A card is drawn from cards numbered 1 to 10. Find the probability of drawing an even number.

Even cards are:

E = {2,4,6,8,10}

Number of favourable outcomes = 5.

Total outcomes = 10.

P({Even}) = (5)/(10)

= (1)/(2)

Q5. A letter is picked from the word PROBABILITY. Find the probability of picking B.

The word PROBABILITY has 11 letters.

The letter B appears 2 times.

P(B) = (2)/(11)

So, the probability is (2/11).

Sample Space Class 9 Important Questions

Sample space class 9 questions test whether students can list outcomes without missing or repeating them. The sample space must match the level of detail required by the question.

Q1. What is sample space?

Sample space is the set of all possible outcomes of a random experiment.

It is usually denoted by (S).

For tossing a coin once:

S = {H,T}

Q2. Write the sample space for rolling a die once.

A standard die has six faces.

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

The sample size is:

n(S) = 6

Q3. Write the sample space for tossing two coins.

The possible outcomes are:

S = {HH, HT, TH, TT}

The sample size is:

n(S) = 4

Q4. Write the sample space for rolling a die and tossing a coin together.

For each die outcome, the coin can show H or T.

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

The sample size is:

n(S) = 12

Q5. Write the sample space for choosing a random integer from -5 to +5.

S = {-5,-4,-3,-2,-1,0,1,2,3,4,5}

The sample size is:

n(S) = 11

Events in Probability Class 9 Question Answer

Events in probability class 9 questions ask students to identify the favourable outcomes from the sample space. An event may contain one outcome or many outcomes.

Q1. What is an event in probability?

An event is any single outcome or group of outcomes from a sample space.

For rolling a die, the event “getting a number greater than 4” is:

E = {5,6}

Q2. In tossing two coins, write the event of getting at least one head.

Sample space:

S = {HH, HT, TH, TT}

Event of at least one head:

E = {HH, HT, TH}

So:

P(E) = (3)/(4)

Q3. In rolling a die, write the event of getting an odd number.

Odd numbers on a die are:

E = {1,3,5}

So:

P({Odd}) = (3)/(6)

= (1)/(2)

Q4. In picking a fruit from apple, banana and orange, write the event of selecting a yellow fruit.

Sample space:

S = {{Apple, Banana, Orange}}

The yellow fruit is banana.

E = {{Banana}}

Q5. A bag has 3 red balls, 2 blue balls and 1 green ball. Find the probability that the ball is not red.

Total balls:

3 + 2 + 1 = 6

Not red balls:

2 + 1 = 3

P({Not red}) = (3)/(6)

= (1)/(2)

Tree Diagram Probability Class 9 Important Questions

Tree diagram probability class 9 questions help list outcomes in multi-step experiments. Each complete path gives one outcome.

Q1. Why are tree diagrams useful in probability?

Tree diagrams help list all possible outcomes in a multi-step experiment.

They are useful for coin tosses, repeated draws, choosing combinations and probability questions with more than one stage.

Q2. Draw the sample space for tossing a coin twice using a tree idea.

First toss: H or T.

Second toss after each first toss: H or T.

Sample space:

S = {HH, HT, TH, TT}

Each outcome has probability:

(1)/(4)

Q3. What is the probability of getting one head and one tail when tossing two coins?

Sample space:

S = {HH, HT, TH, TT}

One head and one tail:

E = {HT, TH}

P(E) = (2)/(4)

= (1)/(2)

Q4. Three coins are tossed. Find the probability of getting exactly two heads.

Sample space:

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

Exactly two heads:

E = {HHT, HTH, THH}

P(E) = (3)/(8)

Q5. A child has 2 shirts and 3 pants. How many outfit combinations are possible?

Each shirt can pair with 3 pants.

Total combinations:

2 × 3 = 6

If shirts are Red and Blue, and pants are Jeans, Khakis and Shorts, the combinations are Red-Jeans, Red-Khakis, Red-Shorts, Blue-Jeans, Blue-Khakis and Blue-Shorts.

Independent Events and Gambler’s Fallacy in Class 9 Probability

Independent events are important because previous results do not change the probability of the next fair coin toss or die roll. Students often make mistakes here.

Q1. What are independent events?

Independent events are events where the result of one event does not affect the result of another.

For example, getting heads on one fair coin toss does not affect the next toss.

Q2. If a coin shows heads five times in a row, is tails more likely on the next toss?

No, tails is not more likely.

For a fair coin, each toss is independent. The probability of heads and tails remains (1/2) on the next toss.

Q3. What is Gambler’s Fallacy?

Gambler’s Fallacy is the mistaken belief that past results change the next outcome in an independent random experiment.

For example, after many heads, someone may think tails is “due”. This is wrong for a fair coin.

Q4. A fair die has not shown 6 in ten rolls. Is 6 more likely on the next roll?

No, 6 is not more likely.

Each die roll is independent. The probability of getting 6 remains (1/6).

Q5. Why is replacement important in probability questions?

Replacement decides whether the second trial has the same sample space.

If an object is replaced, the probabilities stay the same. If it is not replaced, the total number of objects changes.

Class 9 Maths Chapter 7 MCQ with Answers

Class 9 Maths Chapter 7 MCQ questions test probability scale, sample space and quick calculation. Read each option carefully before choosing.

Q1. Probability of an impossible event is:

(a) 1

(b) 0

(c) 1/2

(d) 2

Answer: (b) 0

An impossible event cannot occur.

Q2. Probability of a certain event is:

(a) 0

(b) 1/4

(c) 1

(d) 2

Answer: (c) 1

A certain event will definitely happen.

Q3. The sample space for tossing one coin is:

(a) {H}

(b) {T}

(c) {H, T}

(d) {HH, TT}

Answer: (c) {H, T}

A coin has two possible outcomes.

Q4. The probability of getting heads on a fair coin is:

(a) 0

(b) 1/2

(c) 1

(d) 2

Answer: (b) 1/2

Heads and tails are equally likely.

Q5. The probability of rolling a number greater than 6 on a fair die is:

(a) 0

(b) 1/6

(c) 1/2

(d) 1

Answer: (a) 0

A standard die has numbers only from 1 to 6.

Q6. The event “getting a number less than 9” on a spinner numbered 1 to 8 is:

(a) Impossible

(b) Less likely

(c) Certain

(d) Even chance

Answer: (c) Certain

All numbers from 1 to 8 are less than 9.

Class 9 Maths Chapter 7 Extra Questions with Answers

Class 9 maths chapter 7 extra questions help students practise sample space, event selection and probability calculation.

Q1. Two coins are tossed together. Find the probability of getting at least one head.

Sample space:

S = {HH, HT, TH, TT}

At least one head:

E = {HH, HT, TH}

P(E) = (3)/(4)

Q2. A bag contains 3 candies: strawberry, lemon and mint. Find the probability of picking strawberry.

Total candies = 3.

Favourable candy = 1.

P({Strawberry}) = (1)/(3)

Q3. The letters of PEACE are placed on cards. Find the probability of drawing P, E or C.

The word PEACE has 5 letters.

P appears once, E appears twice, and C appears once.

Favourable outcomes:

1 + 2 + 1 = 4

P(P,E { or } C) = (4)/(5)

Q4. In the word PEACE, find the probability of not drawing E.

Total letters = 5.

E appears 2 times.

Not E letters = P, A, C = 3.

P({Not E}) = (3)/(5)

Q5. A spinner has numbers 1 to 8. Find the probability of getting an odd number.

Odd numbers:

E = {1,3,5,7}

Total outcomes = 8.

P({Odd}) = (4)/(8)

= (1)/(2)

Q6. A spinner has numbers 1 to 8. Find the probability of getting a multiple of 3.

Multiples of 3 from 1 to 8 are:

E = {3,6}

P({Multiple of 3}) = (2)/(8)

= (1)/(4)

Statistical Probability Class 9 Application Questions

Statistical probability uses collected data. Students should use the data exactly as given.

Q1. A survey of 40 students shows 14 prefer Science Club, 11 Arts Club, 9 Sports Club and 6 Debate Club. Find the probability that a student prefers Arts Club.

Number of Arts Club students = 11.

Total students = 40.

P({Arts Club}) = (11)/(40)

So, the probability is (11/40).

Q2. In the same survey, estimate how many students prefer Sports Club if the school has 800 students.

Sports Club students in sample = 9.

Total sample = 40.

P({Sports Club}) = (9)/(40)

Estimated number:

(9)/(40) × 800 = 180

So, about 180 students may prefer Sports Club.

Q3. A tyre company records 1000 cases. 20 tyres last less than 4000 km. Find the probability.

P({Less than 4000 km}) = (20)/(1000)

= (1)/(50)

= 0.02

Q4. In the same data, 210 tyres last 4001 to 9000 km and 325 tyres last 9001 to 14000 km. Find the probability of lasting between 4000 and 14000 km.

Number of cases:

210 + 325 = 535

Total cases = 1000.

P = (535)/(1000)

= 0.535

Q5. In the same data, 445 tyres last more than 14000 km. Find the probability.

P({More than 14000 km}) = (445)/(1000)

= 0.445

Long Answer Questions from Class 9 Maths Chapter 7

Long answers should explain the concept and show the calculation step by step.

Q1. Explain the difference between experimental probability and theoretical probability.

Experimental probability is based on actual trials or collected data.

{Experimental Probability} = frac{{Number of times the event occurred}}{{Total number of trials}}

For example, if a die is rolled 12 times and 3 appears 3 times:

P(3) = (3)/(12) = (1)/(4)

Theoretical probability is based on equally likely outcomes in a fair situation.

P(E) = frac{{Number of favourable outcomes}}{{Number of possible outcomes}}

For a fair die:

P(3) = (1)/(6)

Both probabilities may differ when the number of trials is small. With many trials, experimental probability usually gets closer to theoretical probability.

Q2. A die is rolled 12 times and 3 appears 3 times. Find experimental and theoretical probability. Explain why they differ.

Experimental probability:

P(3) = (3)/(12)

= (1)/(4)

Theoretical probability:

P(3) = (1)/(6)

They differ because only 12 trials were performed. In a small number of trials, results can vary from expectation.

If the die is rolled 60, 600 or 6000 times, the experimental probability is expected to move closer to (1/6).

Q3. Two coins are tossed simultaneously. Write the sample space and find the probability of at least one head.

Sample space:

S = {HH, HT, TH, TT}

Event of at least one head:

E = {HH, HT, TH}

Number of favourable outcomes = 3.

Total outcomes = 4.

P(E) = (3)/(4)

So, the probability of at least one head is (3/4).

Q4. Three coins are tossed simultaneously. Find the probability of exactly two heads.

Sample space:

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

Total outcomes = 8.

Exactly two heads:

E = {HHT, HTH, THH}

Number of favourable outcomes = 3.

P(E) = (3)/(8)

So, the probability is (3/8).

Q5. A bag contains 4 red balls and 5 blue balls. One ball is drawn and kept aside. A second ball is drawn. Find the probability of drawing a red ball and then a blue ball.

Total balls = 9.

Probability of drawing red first:

(4)/(9)

After one red ball is removed, 8 balls remain.

Blue balls = 5.

Probability of drawing blue second:

(5)/(8)

So:

P({Red then Blue}) = (4)/(9) × (5)/(8)

= (20)/(72)

= (5)/(18)

So, the probability is (5/18).