Probability Class 9 Notes: Complete NCERT Guide, HOTS, MCQs & Practice Questions
Introduction
Probability’s one of the most interesting topics in Mathematics. It helps us predict the chances of an event occurring in daily life. Whether it is tossing a coin, rolling a dice, drawing a card, or forecasting weather conditions, probability plays an important role in decision-making. ( Probability Class 9)
प्रायिकता (Probability) गणित का एक महत्वपूर्ण अध्याय है जो किसी घटना के होने की संभावना को दर्शाता है। यह अध्याय विद्यार्थियों को तार्किक सोच विकसित करने में मदद करता है तथा प्रतियोगी परीक्षाओं की तैयारी के लिए भी अत्यंत उपयोगी है।
Class 10 STRATEGY & HIGH SCORE TIPS
Table of Contents
- What is Probability?
- Important Terms
- Abbreviations
- Formula of Probability
- Key Points
- Solved Examples
- NCERT Questions with Solutions
- HOTS Questions
- Tricky Questions
- Word Problems
- MCQs for Practice
- Quick Revision Notes
- Reader Challenge
- Conclusion
Abbreviations
| Abbreviation | Full Form |
|---|---|
| P(E) | Probability of Event E |
| S | Sample Space |
| F.O. | Favourable Outcomes |
| T.O. | Total Outcomes |
| NCERT | National Council of Educational Research and Training |
| HOTS | Higher Order Thinking Skills |
| MCQ | Multiple Choice Question |
What is Probability?
Probability is the numerical measure of the likelihood of an event occurring.
Formula
Probability of an Event
P(E) = Number of Favourable Outcomes / Total Number of Outcomes
हिंदी में
प्रायिकता किसी घटना के होने की संभावना का संख्यात्मक मान है।
प्रायिकता = अनुकूल परिणामों की संख्या ÷ कुल परिणामों की संख्या
Important Terms
Experiment (प्रयोग)
A process that produces outcomes.
Example: Tossing a coin.
Outcome (परिणाम)
Result obtained from an experiment.
Example: Head or Tail.
Event (घटना)
A collection of outcomes.
Example: Getting an even number on a dice.
Sample Space (प्रतिदर्श समुच्चय)
Set of all possible outcomes.
Example:
S = {1,2,3,4,5,6}
Key Points.
| It ( Probability ) lies between 0 and 1. |
| Probability of an impossible event = 0 |
| Total probability of all outcomes = 1 |
| Probability of a sure event = 1 |
| Probability can never be negative. |
| It helps in making predictions. |
Solved Examples
Example 1
A coin is tossed once. Find the probability of getting Head.
Solution
Sample Space = {H,T}
Total Outcomes = 2
Favourable Outcomes = 1
P(H) = 1/2
Answer = 1/2
Example 2
A die is rolled once. Find probability of getting 5.
Solution
Sample Space = {1,2,3,4,5,6}
Favourable Outcomes = 1
Total Outcomes = 6
Probability = 1/6
Answer = 1/6
NCERT Questions with Solutions
Question 1
A card numbered 1 to 20 is drawn at random.
Find probability of getting a multiple of 5.
Solution
Multiples of 5 = 5,10,15,20
Favourable Outcomes = 4
Total Outcomes = 20
Probability = 4/20
= 1/5
Answer = 1/5
Question 2
A die is rolled.
Find probability of getting a prime number.
Solution
Prime Numbers = 2,3,5
Favourable Outcomes = 3
Total Outcomes = 6
Probability = 3/6
= 1/2
Answer = 1/2
Question 3
A letter is chosen from the word SCHOOL.
Find probability of getting O.
Solution
Total Letters = 6
Number of O = 2
Probability = 2/6
= 1/3
Answer = 1/3
HOTS Questions
HOTS 1
Two coins are tossed simultaneously.
Find probability of getting exactly one Head.
Solution
Sample Space
{HH, HT, TH, TT}
Favourable Outcomes
HT, TH
Probability = 2/4
= 1/2
HOTS 2
A bag contains 7 red, 5 blue and 8 green balls.
Find probability of drawing a green ball.
Solution
Total Balls = 20
Green Balls = 8
Probability = 8/20
= 2/5
HOTS 3
A number is selected from 1 to 100.
Find probability that it is divisible by both 2 and 5.
Solution
Numbers divisible by 10 = 10
Probability = 10/100
= 1/10
Tricky Questions
Question 1
A die is rolled.
Find probability of getting a number greater than 2 but less than 6.
Solution
Numbers = 3,4,5
Probability = 3/6
= 1/2
Question 2
A card numbered 1 to 30 is selected.
Find probability of getting a perfect square.
Solution
Perfect Squares = 1,4,9,16,25
Probability = 5/30
= 1/6
Question 3
Probability of getting a vowel from the word EDUCATION.
Solution
Total Letters = 9
Vowels = E,U,A,I,O
Count = 5
Probability = 5/9
Word Problems
Problem 1
A basket contains 12 mangoes and 18 apples.
Find probability of selecting an apple.
Solution
Probability = 18/30
= 3/5
Problem 2
A bag contains 4 white, 6 black and 10 red balls.
Find probability of drawing a black ball.
Solution
Probability = 6/20
= 3/10
Problem 3
A class has 15 boys and 20 girls.
Find probability of selecting a girl.
Solution
Probability = 20/35
= 4/7
MCQs for Practice ( Probability Class 9)
1. Probability of getting Head on a coin toss?
A) 0
B) 1
C) 1/2
D) 2
Answer: C
2. Probability of getting an even number on a die?
A) 1/2
B) 1/3
C) 2/3
D) 1
Answer: A
3. Probability of a sure event?
A) 0
B) 1
C) 1/2
D) 2
Answer: B
4. Probability always lies between
A) -1 and 1
B) 0 and 1
C) 1 and 2
D) -2 and 2
Answer: B
5. Which is an impossible event?
A) Sun rising in East
B) Getting number 7 on standard die
C) Tossing Head
D) Rolling number 5
Answer: B
Quick Revision Notes ( Probability Class 9)
- Probability = Favourable Outcomes ÷ Total Outcomes
- Impossible Event = 0
- Sure Event = 1
- Sample Space contains all outcomes
- Probability is never negative
- Sum of probabilities of all outcomes = 1
Reader Challenge Zone ( Probability Class 9)
Solve these questions and submit your answers.
Question 1
A die is rolled. Find probability of getting an odd number.
Question 2
Two coins are tossed. Find probability of getting two Heads.
Question 3
A bag contains 5 red, 4 blue and 6 green balls. Find probability of drawing a blue ball.
Question 4
A card numbered 1 to 50 is selected. Find probability of getting a multiple of 7.
Question 5
A letter is chosen from the word PROBABILITY. Find probability of getting the letter B.
Conclusion
Probability is an important chapter that helps students understand uncertainty and decision-making. By mastering NCERT questions, HOTS problems, tricky questions, and real-life applications, students can score excellent marks in examinations.
🎉 Special Reader Contest
Solve all 5 Reader Challenge Questions and submit your answers through the comment section of Rising Star Mindset.
The best entries will have their Name and Location featured on:
under the “Probability Challenge Winners” section.
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