Experimental probability: Class 9 practice
Experimental (empirical) probability = number of times an event happened ÷ total number of trials. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Fractions
- Frequency tables
The idea behind experimental probability
Experimental (empirical) probability = number of times an event happened ÷ total number of trials. It gets closer to the theoretical value as the number of trials grows.
Step-by-step method
- Find the total number of trials.
- Count the outcomes for the event.
- Divide and simplify.
Worked example 1 (Basic)
In 156 trials the outcomes were 0 heads: 16, 1 head: 56, 2 heads: 56, 3 heads: 28. Find P(0 heads).
- 16/156
- Answer: 4/39
Worked example 2 (Standard)
In 142 trials the outcomes were 0 heads: 6, 1 head: 31, 2 heads: 22, 3 heads: 27, 4 heads: 56. Find P(4 heads).
- 56/142
- Answer: 28/71
Worked example 3 (Challenge)
Coins were tossed 252 times with results 0 heads: 51, 1 head: 54, 2 heads: 58, 3 heads: 35, 4 heads: 27, 5 heads: 27. Find the probability of getting at least one head.
- Favourable = 201
- 201/252
- Answer: 67/84
Common mistakes and misconceptions
- Dividing by the number of categories
- Using the theoretical probability instead
Practice questions
- (Basic) In 83 trials the outcomes were 0 heads: 26, 1 head: 16, 2 heads: 10, 3 heads: 31. Find P(1 head).
- (Basic) In 88 trials the outcomes were 0 heads: 14, 1 head: 19, 2 heads: 39, 3 heads: 16. Find P(3 heads).
- (Standard) In 128 trials the outcomes were 0 heads: 9, 1 head: 25, 2 heads: 18, 3 heads: 31, 4 heads: 45. Find P(4 heads).
- (Standard) In 108 trials the outcomes were 0 heads: 7, 1 head: 13, 2 heads: 18, 3 heads: 36, 4 heads: 34. Find P(4 heads).
- (Challenge) Coins were tossed 205 times with results 0 heads: 18, 1 head: 38, 2 heads: 12, 3 heads: 42, 4 heads: 59, 5 heads: 36. Find the probability of getting at least one head.
- (Challenge) Coins were tossed 174 times with results 0 heads: 18, 1 head: 46, 2 heads: 8, 3 heads: 43, 4 heads: 51, 5 heads: 8. Find the probability of getting at least one head.
Answer key with full working
- Q1: 16/83 → Answer: 16/83
- Q2: 16/88 → Answer: 2/11
- Q3: 45/128 → Answer: 45/128
- Q4: 34/108 → Answer: 17/54
- Q5: Favourable = 187 → 187/205 → Answer: 187/205
- Q6: Favourable = 156 → 156/174 → Answer: 26/29
Syllabus note
This skill is listed under "Probability" for Class 9 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is experimental probability in?
"Probability", Class 9 Maths (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.