Question

Let two dice be thrown. What is the probability that the sum on the dice is greater than
or equal to 9?

Answer 1

Answer on Question #40055, Math, Statistics and Probability

Let two dice be thrown. What is the probability that the sum on the dice is greater than or equal to 9?

Solution

The sample space $S$ of two dice is shown below.

$$S = \{(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)$$ $$(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)$$ $$(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)$$ $$(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)$$ $$(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)$$ $$(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6) \}$$

Let $E$ be the event "sum greater than or equal to 9". Ten possible outcomes give a sum greater than or equal to 9:

$$E = \{(3, 6), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 3), (6, 4), (6, 5), (6, 6)\},$$ $$P (E) = \frac {n (E)}{n (S)} = \frac {1 0}{3 6} = \frac {5}{1 8}.$$

Answer: $\frac{5}{18}$