Class 9 Maths · Original EZT practice
Introduction to Probability (Class 9 Chapter 7): summary and practice
Probability is how maths talks about chance. This chapter introduces it properly: what randomness means, the 0 to 1 probability scale, the difference between experimental and theoretical probability, and how sample spaces organise every possible outcome. All questions are original EZT tutor practice following the chapter's own section order.
6 original worked examples, 6 fresh self-check questions and 4 mixed questions, with explained answers. These are not copied textbook exercises, an official chapter index or a full answer key. No affiliation with NCERT is claimed.
Official sources for topic and edition context, checked 22 October 2026:
1. Randomness and the probability scale
A situation is random when we know every possible outcome but cannot predict which will occur - a coin toss, a die roll. Probability places events on a scale: 0 impossible, 1 certain, 0.5 equally likely either way.
2. Experimental probability
Repeat the experiment many times and count: experimental probability = times the event occurred / total trials. It is an estimate from observed data that settles closer to the theoretical value as trials grow.
3. Theoretical probability and sample spaces
The sample space lists every possible outcome. When outcomes are equally likely, theoretical probability = favourable outcomes / total outcomes - like 3 even faces out of 6 on a die.
4. Organising outcomes
For multi-step experiments the chapter organises outcomes systematically, including tree diagrams - branch once per step so no outcome is missed and counting favourable cases stays honest.
Choose, solve, check, then try a fresh question.
Before calculating, read the method prompt and name the condition that makes it useful. Write your own attempt. Open the steps only when you need them, and use the check to catch a wrong sign, unit or interpretation. Finish with the fresh question before reading its answer.
Read the probability scale
Choose the method: 0 impossible, 1 certain, 0.5 a coin-flip.
EZT practice question
Your school's probability of winning the hockey match is 0.5. What does that mean?
Show the worked solution
- Probability 0 would mean winning is impossible.
- Probability 1 would mean winning is certain.
- 0.5 sits halfway - winning and losing are equally likely, a 50% chance.
Answer: Winning and losing are equally likely - a 50% chance.
Check: Place two more on the scale: the sun rising tomorrow sits at 1 (certain); rolling a 7 on a standard die sits at 0 (impossible - the faces are 1 to 6).
Watch for this: No event has probability greater than 1 - 1 already means certain, and nothing beats certain.
Now try it yourself
Can a probability be -0.2?
Check your answer
No.
The scale runs only from 0 to 1.
Compute an experimental probability
Choose the method: Divide the count of the event by the number of trials.
EZT practice question
A coin is tossed 200 times and lands heads 104 times. What is the experimental probability of heads?
Show the worked solution
- Experimental probability = times the event occurred / total trials.
- That is 104 / 200.
- Which simplifies to 0.52.
Answer: 104/200 = 0.52.
Check: 0.52 sits near the theoretical 0.5 - with 200 trials the observed fraction is usually close, and it drifts nearer as trials grow.
Watch for this: Do not round the experiment to the theory - report what the data says: 0.52, not 0.5.
Now try it yourself
A die is rolled 60 times and shows a 6 on 9 rolls. Experimental probability of a 6?
Check your answer
9/60 = 0.15.
Event count over total trials.
Why experiment and theory differ
Choose the method: Small samples wander; large samples settle.
EZT practice question
Why might the experimental probability of heads differ from 0.5 in a small number of tosses?
Show the worked solution
- Each toss is random, so short runs are lumpy.
- In 10 tosses, 7 heads is perfectly ordinary - giving 0.7.
- With thousands of tosses the fraction settles near 0.5.
Answer: Random variation - few trials can drift from the theoretical value.
Check: This is exactly why the chapter measures probability objectively through many trials: the estimate improves as the count grows.
Watch for this: A weird short run does not prove the coin is unfair - drift is expected.
Now try it yourself
Which estimate is more trustworthy: 100 tosses or 10000?
Check your answer
10000.
More trials settle closer to the true value.
Compute a theoretical probability
Choose the method: Count favourable outcomes over total equally likely outcomes.
EZT practice question
A fair die is rolled once. What is the probability of getting an even number?
Show the worked solution
- Sample space: 1, 2, 3, 4, 5, 6 - six equally likely outcomes.
- Even outcomes: 2, 4, 6 - three of them.
- Probability = 3/6 = 1/2 = 0.5.
Answer: 3/6 = 1/2 = 0.5.
Check: Favourable over total is the whole method - listing the sample space first keeps the count honest.
Watch for this: Do not count outcomes twice or skip one - write the sample space out.
Now try it yourself
A fair coin is tossed once. Probability of tails?
Check your answer
1/2 = 0.5.
One favourable outcome out of two.
Sample space with unequal counts
Choose the method: Each ball is one equally likely outcome.
EZT practice question
A bag has 3 red and 2 blue balls, identical except for colour. One ball is drawn at random. What is the probability it is blue?
Show the worked solution
- Five balls, each equally likely to be drawn - the sample space has 5 outcomes.
- Blue is favourable in 2 of them.
- Probability = 2/5 = 0.4.
Answer: 2/5 = 0.4.
Check: Counts, not colours, make the outcomes: 3 + 2 = 5 total, 2 favourable - the fraction follows.
Watch for this: Do not answer 1/2 - the two colours are not equally likely when their counts differ.
Now try it yourself
Same bag - probability of red?
Check your answer
3/5 = 0.6.
3 favourable out of 5.
Define the sample space
Choose the method: List every possible outcome before counting.
EZT practice question
What is the sample space of a single die roll, and why does it matter?
Show the worked solution
- The sample space is the list of all possible outcomes.
- For one die: {1, 2, 3, 4, 5, 6}.
- Every probability in the experiment is favourable-count over this total - so the list must be complete.
Answer: {1, 2, 3, 4, 5, 6} - the complete list of outcomes.
Check: Probabilities computed from a complete sample space always sit between 0 and 1, and all outcome probabilities add to 1.
Watch for this: Missing an outcome breaks every fraction - completeness first, counting second.
Now try it yourself
Sample space of one coin toss?
Check your answer
{heads, tails}.
Those are the only two outcomes.
Try a mixed set
Choose a method or explanation before opening each answer.
1. Probability scale?
Show answer and reason
0 impossible to 1 certain.
0.5 means equally likely either way.
2. Experimental probability?
Show answer and reason
Event count / total trials.
An estimate from observed data.
3. Theoretical probability?
Show answer and reason
Favourable / total equally likely outcomes.
Counted from the sample space.
4. Sample space?
Show answer and reason
All possible outcomes of the experiment.
For a die: {1, 2, 3, 4, 5, 6}.
Try it yourself
Work these on paper before checking any notes. Answers are deliberately not shown here.
- Place on the scale: drawing a red card from a standard deck.
- A die is rolled 100 times and shows a 3 on 18 rolls - find the experimental probability.
- A bag holds 4 green and 1 yellow ball. What is the probability of yellow?
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Questions about this practice page
- What is probability in Class 9 maths?
- Probability measures how likely an event is, on a scale from 0 (impossible) to 1 (certain). A probability of 0.5 means the event is equally likely to happen or not.
- What is the difference between experimental and theoretical probability?
- Experimental probability comes from repeating an experiment and counting outcomes; theoretical probability counts equally likely outcomes in the sample space. With many trials the experimental value tends to approach the theoretical one.
- What is a sample space?
- The list of all possible outcomes of a random experiment - for a single die roll it is {1, 2, 3, 4, 5, 6}. Complete listing comes before counting favourable cases.
- Can a probability be greater than 1?
- No. A probability of 1 already means the event is certain, and nothing is more likely than certain. Probabilities also never go below 0, which means impossible.
- Are these the NCERT exercise questions for Class 9 Maths Chapter 7?
- No. EZT pages are original practice following the chapter's section order - use them to prepare for the textbook exercises, not as a substitute for your book.