Sum of two dice is 8 — Probability Aptitude Question
Sum of two dice is 8: Two fair dice are thrown. What is the probability that the sum is 8? Answer and worked solution on CodeKairo.
- Topic: Probability
- Section: Quantitative Aptitude
- Difficulty: Easy
- Time target: 60 seconds
Question
Two fair dice are thrown. What is the probability that the sum is 8?
Options
- 1/9
- 5/36
- 1/6
- 7/36
Show the answer and the worked solution
Correct answer: B. 5/36
Worked solution
- Pairs summing to 8: (2,6), (3,5), (4,4), (5,3), (6,2) — 5 outcomes.
- Probability = 5/36.
Answer: 5/36.
The idea
For two dice, the number of ways to reach a sum s is s − 1 for s ≤ 7 and 13 − s for s ≥ 7. Sum 8 therefore has 5 ways.
Shortcut. Sum 8 sits one step from the peak at 7, which has 6 ways, so it has 5: 5/36. Sums equally far from 7, such as 6 and 8, always share a count.
Common trap. "1/6" — listing (2,6), (3,5), (4,4) and doubling all three for order; (4,4) has no reverse, so the count is 5, not 6.