Two dice: sums and doubles: Class 10 practice
Throwing two dice gives 36 equally likely ordered outcomes. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Basic probability
The idea behind two dice: sums and doubles
Throwing two dice gives 36 equally likely ordered outcomes. Count the pairs that satisfy the condition, e.g. sum = 7 has 6 pairs.
Step-by-step method
- List or picture the 6 × 6 grid.
- Count favourable ordered pairs.
- Divide by 36 and simplify.
Worked example 1 (Basic)
Two dice are thrown. Find P(sum = 2).
- Favourable pairs: 1
- P = 1/36
- Answer: 1/36
Worked example 2 (Standard)
Two dice are thrown. Find P(sum is at least 5).
- Count pairs with sum ≥ 5: 30
- P = 5/6
- Answer: 5/6
Worked example 3 (Challenge)
Two dice are thrown. Find P(a doublet or a product divisible by 2).
- Count pairs satisfying either condition: 30
- P = 5/6
- Answer: 5/6
Common mistakes and misconceptions
- Counting (2,5) and (5,2) as one
- Using 11 outcomes for sums
Practice questions
- (Basic) Two dice are thrown. Find P(sum = 6).
- (Basic) Two dice are thrown. Find P(sum = 9).
- (Standard) Two dice are thrown. Find P(sum is at least 9).
- (Standard) Two dice are thrown. Find P(sum is at least 10).
- (Challenge) Two dice are thrown. Find P(a doublet or a product divisible by 3).
- (Challenge) Two dice are thrown. Find P(a doublet or a product divisible by 4).
Answer key with full working
- Q1: Favourable pairs: 5 → P = 5/36 → Answer: 5/36
- Q2: Favourable pairs: 4 → P = 1/9 → Answer: 1/9
- Q3: Count pairs with sum ≥ 9: 10 → P = 5/18 → Answer: 5/18
- Q4: Count pairs with sum ≥ 10: 6 → P = 1/6 → Answer: 1/6
- Q5: Count pairs satisfying either condition: 24 → P = 2/3 → Answer: 2/3
- Q6: Count pairs satisfying either condition: 18 → P = 1/2 → Answer: 1/2
Syllabus note
This skill is listed under "Probability" for Class 10 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 two dice: sums and doubles in?
"Probability", Class 10 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.