Sum of two dice is 9 — Probability Aptitude Question
Sum of two dice is 9: Two fair dice are rolled. What is the probability that the sum is 9? Answer and worked solution on CodeKairo.
- Topic: Probability
- Section: Quantitative Aptitude
- Difficulty: Easy
- Time target: 45 seconds
Question
Two fair dice are rolled. What is the probability that the sum is 9?
Options
- 1/12
- 5/36
- 1/6
- 1/9
Show the answer and the worked solution
Correct answer: D. 1/9
Worked solution
- Pairs summing to 9: (3,6), (4,5), (5,4), (6,3) — 4 outcomes.
- Probability = 4/36 = 1/9.
Answer: 1/9.
The idea
For two dice, the number of ways to get a sum s is s − 1 for s ≤ 7 and 13 − s for s ≥ 7. So sum 9 has 4 ways, sum 7 has 6.
Shortcut. Only a first die of 3, 4, 5 or 6 can reach 9, and each has exactly one partner — 4 of 36, i.e. 1/9.
Common trap. 1/6 — the probability for a sum of 7, the figure everyone remembers; a sum of 9 has only 4 ordered pairs, not 6.