ITPEC FE Morning October 2022 Question 3
Topic: Basic Theory
When two dice are rolled, what is the probability that the sum of the dice is 5? Here, the two dice are fair and independent.
Explanation
1/9 — count the ordered outcomes that sum to 5 among the 36 equally likely outcomes.
- •Outcomes of two dice: 6 × 6 = 36, each equally likely because the dice are distinguishable
- •Sum 5: (1, 4), (2, 3), (3, 2), (4, 1), that is 4 outcomes
- •Probability: 4 ÷ 36 = 1 ÷ 9
Answer (c)
Why not others:
- •(a) 1/18 — 2 ÷ 36: counts only the unordered pairs {1, 4} and {2, 3}, while still dividing by the 36 ordered outcomes
- •(b) 1/12 — 3 ÷ 36, the probability of a sum of 4 (or 10), not 5
- •(d) 1/6 — 6 ÷ 36, the probability of a sum of 7, the most likely total
Key rule: Count outcomes the same way in the numerator and the denominator: with 36 ordered outcomes, (1, 4) and (4, 1) are two different outcomes.
Basic Theory · AI-written, may contain errors
This question comes from an official ITPEC past paper. ITPEC Practice is an independent study tool and is not affiliated with ITPEC. See the official FE past-paper collection or Report an issue.