Two dice are rolled together. Find the probability that (i) the sum is greater than 9 (ii) the sum is a prime number (iii) the product of the numbers is 12.
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, so n(S) = 6 × 6 = 36. To find: three probabilities.
2 · Write out the sample space Make a 6 × 6 table of sums, with the first die down the side and the second die across the top.
3 · Write the formula P(E) = n(E)/n(S).
4 · Part (i): sum greater than 9
Sum 10: (4, 6), (5, 5), (6, 4); sum 11: (5, 6), (6, 5); sum 12: (6, 6)
n(A) = 6, so P(A) = 6/36 = 1/6
5 · Part (ii): prime sum
The prime sums 2, 3, 5, 7 and 11 occur 1 + 2 + 4 + 6 + 2 = 15 times
P(B) = 15/36 = 5/12
6 · Part (iii): product 12
Product 12: (2, 6), (3, 4), (4, 3), (6, 2)
n(C) = 4, so P(C) = 4/36 = 1/9
7 · Check and box the answer P(A) = 1/6, P(B) = 5/12, P(C) = 1/9. Each answer lies between 0 and 1.
Scoring tip: List the favourable pairs in brackets. (4, 6) and (6, 4) are different outcomes, so write both.
