Question

Find the probability that the sum is as stated when a pair of dice is rolled. (Enter your answers as fractions.)

(a) odd or less than 5

Answer 1

Since each dice has 6 faces, the total number of outcomes is

$n = 6 \cdot 6 = 36$

Let's list the favorable outcomes: (1,1), (1,2), (1,3), (1,4), (1,6), (2,1), (2,2), (2,3), (2,5), (3,1), (3,2), (3,4), (3,6), (4,1), (4,3), (4,5), (5,2), (5,4), (5,6), (6,1), (6,3), (6,5).

Then the number of favorable outcomes $m = 22$ . So, $p = \frac{m}{n} = \frac{{22}}{{36}} = \frac{{11}}{{18}}$ .

Answer: $p = \frac{{11}}{{18}}$