TEACHGYAN • CLASS 10 MATHEMATICS • NCERT 2026–27
Chapter 14: Probability
Detailed Notes • Worked Examples • Competency • Board Practice
📖 Chapter Explanation
Probability provides a numerical measure of uncertainty. Students calculate probabilities of events, use complementary events and apply counting ideas to familiar experiments while checking that probabilities lie between 0 and 1.
🧭 Concept Journey
📌 Core Concepts
For equally likely outcomes, P(E)=favourable outcomes/total outcomes and P(not E)=1−P(E). Probability 0 represents impossibility and probability 1 represents certainty.
💡 Worked Example
For a fair die, P(number greater than 4)=2/6=1/3 because the favourable outcomes are 5 and 6.
🔍 Why the Method Works
For equally likely outcomes, P(E)=favourable outcomes/total outcomes and P(not E)=1−P(E). Probability 0 represents impossibility and probability 1 represents certainty.
⚠️ Common Errors
Never count outcomes without defining the sample space. Check whether outcomes are equally likely before using the simple ratio formula.
🧠 Concept-Based MCQs
- A probability must lie between: A) −1 and 1 B) 0 and 1 C) 1 and 100 D) any two numbers
- P(not E) equals: A) P(E)−1 B) 1−P(E) C) 1/P(E) D) P(E)+1
- For a fair coin, P(heads)=: A) 0 B) 1/4 C) 1/2 D) 1
- An impossible event has probability: A) 0 B) 1/2 C) 1 D) −1
Answer Key: 1-B, 2-B, 3-C, 4-A.
📊 Case-Based / Competency
A game awards a prize when a randomly selected card is red or when a die shows a specified result. Students define the sample space, identify favourable outcomes and calculate the relevant probabilities.
- Identify the information and variables.
- Select the appropriate mathematical model.
- Calculate step by step.
- Interpret and verify the result.
🔎 Extension Case
A school conducts a probability game using coloured cards and a fair die. Students construct the sample space, calculate event probabilities and compare theoretical probability with results from repeated trials.
🔥 HOTS & Board Challenge
- Explain why the selected formula or method is appropriate.
- Create a similar problem and solve it.
- Find and correct a plausible incorrect solution.
- Apply the concept in a new context.
✍️ Exam Practice
- Define the central concept.
- Solve a direct application problem.
- Solve a multi-step competency problem.
- Interpret a diagram/table/context.
- Write a complete 5-mark solution with reasoning.
📄 Practice Worksheet
- 5 concept checks
- 5 standard problems
- 3 applications
- 2 case-based questions
- 2 HOTS questions
- 1 board-style challenge
🎯 One-Minute Revision
sample space → event → favourable outcomes → probability → complement → combined reasoning
🏆 Mastery Checklist
- ☐ I understand the concept.
- ☐ I can select the correct method.
- ☐ I can solve step by step.
- ☐ I can handle competency questions.
- ☐ I can verify and interpret my answer.
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Original explanatory study material aligned to NCERT/CBSE topics; textbook passages are not reproduced verbatim.