College Algebra, Chapter 10, 10.3, Section 10.3, Problem 10

Suppose that a die is rolled. Determine the probability of the given event.

a.) The number showing is a two or three.

The probability of showing a two on a die is $\displaystyle P(2) = \frac{1}{6}$. Similarly, the probability of showing a three on a die is also $\displaystyle P(3) = \frac{1}{6}$. Since we have mutually exclusive events, we get

$\displaystyle P(2) + P(3) = \frac{1}{6} + \frac{1}{6} = \frac{2}{6} + \frac{1}{3}$

b.) The number showing is an odd number..

The odd numbers on the sample space $n(S) = \{ 1,2,3,4,5,6 \}$ are $1,3$ and $5$. Thus, the probability of getting an odd number is

$\displaystyle \frac{3}{6} = \frac{1}{2}$

c.) The number showing is a number divisible by 3.

The numbers are divisible by 3 in the sample space is $3$ and $6$. Thus the probability is

$\displaystyle \frac{2}{6} = \frac{1}{3}$