Example 18
Two fair dice are thrown and the number on the top face of each die is recorded. If the score is
taken as the sum of the two recorded numbers, find the probability that the score is

Note: A prime number is a whole number greater than 1 , whose only factors are 1 and itself

When you throw two fair dice, each die has six faces showing the numbers 1 through 6. This creates a total of 36 different combinations (6 x 6).

To calculate the probabilities:

(a) To get a score of 12, the only combination is (6, 6). Thus, the probability is .

(b) The combinations that yield a score of 9 are (3, 6), (4, 5), (5, 4), and (6, 3). That’s four combinations, giving a probability of or simplified, .

© For scores more than 8, the scores can be 9, 10, 11, and 12. We already identified 9: 4 combinations, for 10: (4, 6), (5, 5), (6, 4) = 3 combinations; for 11: (5, 6), (6, 5) = 2 combinations; and for 12: 1 combination. Adding these up gives 4 + 3 + 2 + 1 = 10 combinations. Thus, the probability is or simplified, .

(d) The prime numbers possible from two dice are 3, 5, 7, 11. The combinations for:

Thus, the final probabilities are:
(a)
(b)
©
(d)