Class 9 Maths Chapter 15 Probability Notes
These Class 9 Maths Chapter 15 Probability notes help you revise the idea of chance using experiments, outcomes and events. In CBSE Class 9, probability is introduced mainly through experimental probability: you repeat an activity, record results and calculate how often an event occurs. This chapter is scoring because the formula is simple, but students often lose marks by mixing up outcomes, trials and events or by giving probability outside the range 0 to 1. Use these notes for last-minute revision of definitions, formula use, solved mini-examples and common exam traps. After reading, revise faster with YoLearn AI Tools: create Flashcards for terms like trial and event, generate a Mind Map of formulas, attempt a Quiz on probability values, and use the Summarizer to compress these notes into a final exam sheet.
Key points
- Probability measures the chance of an event happening; in Class 9, it is mainly based on experiments and observations.
- Experimental probability formula: P(E) = Number of trials in which event E occurs / Total number of trials.
- Probability always lies between 0 and 1, including both: 0 ≤ P(E) ≤ 1.
- If P(E) = 0, the event is impossible in the given experiment; if P(E) = 1, the event is certain.
- An outcome is one possible result of a trial; an event is a collection of one or more outcomes.
- The denominator must be the total number of trials, not the number of possible outcomes unless the question is theoretical and equally likely.
- For any event E, P(not E) = 1 - P(E), when E and not E cover all possible cases.
- More trials usually give a more reliable estimate of probability because random fluctuations reduce.
- Probability is written as a fraction, decimal or percentage, but fractions are safest in CBSE answers unless asked otherwise.
- Do not write probability with units; it is a pure number because it is a ratio.
Important definitions
- Trial
- One performance of a random experiment, such as tossing a coin once or rolling a die once.
- Random experiment
- An activity whose result cannot be predicted with certainty before it is performed, even though possible results may be known.
- Outcome
- A possible result of a trial. For example, getting Head in a coin toss is an outcome.
- Event
- A result or group of results about which probability is calculated, such as getting an even number on a die.
- Experimental probability
- Probability found from actual observations or data: number of times an event occurs divided by total number of trials.
- Impossible event
- An event with probability 0; it cannot occur in the given experiment.
- Certain event
- An event with probability 1; it always occurs in the given experiment.
- Complementary event
- The event that E does not occur, written as not E, with probability 1 - P(E).
Core concept: experimental probability
In Class 9, probability is introduced through real observations rather than advanced counting. Suppose a coin is tossed many times. You cannot say with certainty what will appear in the next toss, but after many tosses you can compare the number of Heads with the total number of tosses. This comparison gives experimental probability. The key idea is: probability is a ratio of favourable observations to total observations. If an event E happens 18 times in 50 trials, then P(E) = 18/50 = 9/25. The value must be between 0 and 1 because the number of times an event occurs cannot be negative and cannot exceed the total trials. In exams, first identify the event, then locate its frequency, then divide by total trials.
Formula sheet for Chapter 15 Probability
How to solve a probability question quickly
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Experimental probability vs theoretical probability
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Worked mini-examples
- {"title":"Example 1: Coin toss data","bodyMarkdown":"A coin is tossed 80 times and Head appears 36 times. Find P(Head). Solution: Total trials = 80, favourable trials = 36. P(Head) = 36/80 = 9/20."}
- {"title":"Example 2: Dice observation","bodyMarkdown":"A die is thrown 120 times. An even number appears 54 times. Find probability of getting an even number. Solution: P(even) = 54/120 = 9/20."}
- {"title":"Example 3: Complement probability","bodyMarkdown":"In a survey of 200 students, 130 like mathematics. Find probability that a student does not like mathematics. Solution: Students not liking maths = 200 - 130 = 70. Probability = 70/200 = 7/20. Also, P(not liking) = 1 - 130/200."}
Diagram-friendly explanation: frequency table method
Many CBSE questions give a table of results. Draw three columns in your rough work: Outcome, Frequency, and Event check. Add all frequencies to get the total number of trials. Then tick the rows that satisfy the event. For example, if a table shows marks groups and asks the probability of scoring 60 or more, add frequencies only from groups beginning at 60 and above. The sum of ticked frequencies is the numerator. The total frequency is the denominator. This method prevents the common mistake of selecting only one row when the event includes multiple outcomes.
Exam tips and common mistakes
Marking cues: Write the formula before substituting values; it shows method even if arithmetic slips. Always mention total trials and favourable trials clearly. Common traps: using number of categories as denominator, forgetting to simplify fractions, writing probability greater than 1, adding units like students or times, and confusing 'not E' with E. If a question says 'at least', include the boundary value; if it says 'more than', exclude the boundary. For table questions, first total the frequencies carefully.
Quick revision checks
- Q: What is the formula for experimental probability? A: P(E) = Number of trials in which E occurs / Total number of trials.
- Q: Can probability be 1.25? Why? A: No. Probability always lies between 0 and 1.
- Q: A bulb is tested 50 times and fails 4 times. What is P(failure)? A: 4/50 = 2/25.
- Q: If P(E)=3/5, what is P(not E)? A: 1 - 3/5 = 2/5.
Frequently Asked Questions
What is the main formula in Class 9 Probability?
The main formula is P(E) = number of trials in which event E occurs divided by total number of trials. This is called experimental probability because it is based on observed data.
Why must probability be between 0 and 1?
The number of times an event occurs cannot be less than 0 and cannot be more than the total number of trials. Therefore, the ratio always lies from 0 to 1.
What is the difference between outcome and event?
An outcome is a single possible result, such as getting 4 on a die. An event may include one or more outcomes, such as getting an even number: 2, 4 or 6.
How do I find probability from a frequency table?
First add all frequencies to get total trials. Then add the frequencies that satisfy the required event and divide this by the total frequency.
What should I revise first before the exam?
Revise the formula, range 0 ≤ P(E) ≤ 1, meanings of trial/outcome/event, and complement rule P(not E)=1-P(E). Then practise 3 to 4 table-based questions.