Two dice are thrown at the same time. Find the probability of getting (i) a sum of 10, (ii) a doublet, (iii) a sum that is a prime number.

How to lay out the answer. Follow the frame, then write it in your own words.

1 · Write what is given and what is to be found. Two dice are thrown together. To find: P(sum 10), P(doublet), P(prime sum).
2 · Write the total outcomes. Each die has 6 faces, so there are 6 × 6 = 36 equally likely outcomes.
3 · Write the formula. P(E) = favourable outcomes ÷ 36.
4 · Count for each event.
- Sum 10: (4, 6), (5, 5), (6, 4): 3 outcomes.
- Doublets: (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6): 6 outcomes.
- Prime sums 2, 3, 5, 7, 11: 1 + 2 + 4 + 6 + 2 = 15 outcomes.
5 · Work out each probability.
- P(sum 10) = 3/36 = 1/12.
- P(doublet) = 6/36 = 1/6.
- P(prime sum) = 15/36 = 5/12.
6 · Check and box the answer. Each answer lies between 0 and 1 and is in lowest terms. Box all three.

Scoring tip: For two dice, always write 'total outcomes = 36' on its own line. It is the first step examiners look for.