Sum greater than nine — Probability Aptitude Question
Sum greater than nine: Two dice are thrown. What is the probability that the sum is greater than 9? Answer and worked solution on CodeKairo.
- Topic: Probability
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 75 seconds
Question
Two dice are thrown. What is the probability that the sum is greater than 9?
Options
- 1/6
- 1/9
- 5/36
- 1/4
Show the answer and the worked solution
Correct answer: A. 1/6
Worked solution
- Sum 10: 3 ways; sum 11: 2 ways; sum 12: 1 way.
- Favourable = 6 out of 36.
- Probability = 1/6.
Answer: 1/6.
The idea
For sums above 7, the count of ways is 13 − s. Adding the counts for each qualifying sum is quicker than listing pairs.
Shortcut. Sums above 9 mirror sums below 5 (12 ↔ 2, 11 ↔ 3, 10 ↔ 4), which have 1 + 2 + 3 = 6 ways: 6/36 = 1/6.
Common trap. "1/9" — counting unordered pairs ({4,6}, {5,5}, {5,6}, {6,6}) as 4 of 36; (4,6) and (6,4) are separate outcomes.