A number is chosen at random from 1 to 30. Find the probability that it is (i) a prime number, (ii) a multiple of 7, (iii) a perfect square.

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. Numbers 1 to 30, one chosen at random. To find: P(prime), P(multiple of 7), P(perfect square).
2 · Write the formula. P(E) = number of favourable outcomes ÷ total number of outcomes. Total = 30.
3 · List the favourable outcomes.
- Primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 (10).
- Multiples of 7: 7, 14, 21, 28 (4).
- Perfect squares: 1, 4, 9, 16, 25 (5).
4 · Work out each probability.
- P(prime) = 10/30 = 1/3.
- P(multiple of 7) = 4/30 = 2/15.
- P(perfect square) = 5/30 = 1/6.
5 · Check and box the answer. Each answer lies between 0 and 1 and is in lowest terms. Box all three.

Scoring tip: Write the favourable outcomes as a list. A correct list earns marks even if you slip in the division.