Introduction
HSA Notes brings short, clear, exam focused notes designed to help Class 9 SSC Part One Matric students score 90 plus marks in Punjab Board exams under the New Book 2026 to 2027 session. This page covers Unit 13, Probability, from Exercise 13.1, 13.2 & Review Exercise 13 including finding the probability of a single letter draw and working through the 36 outcomes of rolling two fair dice.
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HSA Notes Features
- Short, easy to remember definitions.
- Step by step solutions for every question.
- Tricks and memory aids for faster revision.
- Exact alignment with the PCTB and PECTAA textbook.
- Probability simplified into a clear, repeatable method.
- Past paper pattern questions included throughout.
- A fast revision format built for last minute review.
- Trusted by Punjab students.
Available Across All Punjab Boards and Top Schools
These notes are built for students across all Punjab Boards, including Lahore, Gujranwala, Rawalpindi, Faisalabad, Bahawalpur, Multan, Sargodha, Sahiwal, and DG Khan, and are used at top schools including The City School, Beaconhouse, Roots International, Lahore Grammar School, Karachi Grammar School, Froebel’s, The Educators, Army Public School, Divisional Public School, and Government Model School.
Exercise 13.1, Q1, Probability of Drawing a Consonant
Six discs are marked with the letters L, M, N, O, P, and U. Of these six, four letters, L, M, N, and P, are consonants, while O and U are vowels. The probability of drawing a consonant is the number of consonants divided by the total number of letters, giving P(consonant) = 4/6, which simplifies to 2/3.
Exercise 13.1, Q2, Probability with Two Fair Dice
Rolling two fair dice together produces 36 equally likely outcomes in total, since each die has 6 faces and 6 × 6 = 36.
| Part | Event | Probability |
|---|---|---|
| i | Sum of the two dice is at least 4 | 33/36, simplified to 11/12 |
| ii | Product of the two dice is between 5 and 10 | 11/36 |
| iii | Difference between the two dice is 4 | 4/36, simplified to 1/9 |
View the PDF for the full outcome table and diagrams behind each part.
How to Find Probability from a Simple List of Outcomes
The probability of an event happening is found by dividing the number of favourable outcomes, the outcomes that satisfy the event, by the total number of possible outcomes.
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For a single draw, like the letters L, M, N, O, P, U, the first step is to count how many outcomes in total exist, and the second step is to count only those outcomes that match the condition given, such as being a consonant. Writing the probability as a fraction of favourable outcomes over total outcomes, and then simplifying that fraction to its lowest terms, is the standard way to present the final answer.
How to Work with the 36 Outcomes of Two Dice
Rolling two dice together is best organised as an ordered pair, the result on the first die and the result on the second die, giving 36 total pairs since each of the 6 values on the first die can combine with each of the 6 values on the second.
For a condition on the sum, list or count the pairs whose two values add up to satisfy the condition; it is often faster to count the pairs that fail the condition and subtract from 36 than to count every pair that succeeds directly, which is the approach behind the 33/36 result for a sum of at least 4.
For a condition on the product, multiply the two values in each pair and check whether the result falls in the required range, counting carefully since small products can be easy to miscount. For a condition on the difference, subtract the smaller value from the larger value in each pair, since difference is always taken as a positive amount, and count how many of the 36 pairs give the required difference. In every case, writing the final probability over 36 first and then simplifying keeps the working clear and reduces the chance of arithmetic slips.
Why This Unit Matters for Your Overall Score
Probability builds directly on counting and fraction skills from earlier in the syllabus, and the two dice setup in particular is one of the most frequently tested patterns in past papers, since it can be adapted into sum, product, and difference questions using the same 36-outcome framework. Getting comfortable listing or counting outcomes systematically, rather than guessing at totals, is the single habit that prevents most probability mistakes on the exam.
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Frequently Asked Questions
How do I calculate a basic probability? Divide the number of favourable outcomes by the total number of possible outcomes, then simplify the resulting fraction.
How many total outcomes are there when rolling two dice? 36, since each of the 6 faces on the first die can pair with each of the 6 faces on the second die.
How do I find the probability of a sum, product, or difference with two dice? Count how many of the 36 possible pairs satisfy the given condition on the sum, product, or difference, then write that count over 36 and simplify.
Are these notes aligned with the PCTB and PECTAA textbook? Yes, these notes are built to exactly match the PCTB and PECTAA New Book for Class 9 Mathematics for the 2025 to 2026 session.
Conclusion
With Exercise 13.1 fully solved, covering single-letter probability and the sum, product, and difference cases for two fair dice, Class 9 students have a strong foundation for Unit 13, Probability. Use these notes alongside regular practice with past papers to build the confidence needed for 90 plus marks in your Punjab Board exam.
Best of luck for your Class 9 Mathematics exam!