College Algebra, Chapter 10, 10.3, Section 10.3, Problem 14

Suppose that a ball is drawn randomly from a jar that contains five red balls, two white balls, and one yellow ball. Find the probability of the given event.

a.) Neither a white nor yellow ball is drawn.

Observe that the probability of having neither a white nor yellow ball drawn from the jar is equal to the number of balls is 8 while the number of red balls is 5. So the probability in this case is

$\displaystyle \frac{5}{8}$

b.) A red, white, or yellow ball is drawn.

The number of white ball is two and the yellow ball is one. The probability in this case is

$\displaystyle \frac{5}{8} + \frac{2}{8} + \frac{1}{8} = \frac{8}{8} = 1$

c.) The ball that is drawn is not white.

We can use the complement of an event to get the required probability. The chance of getting a white ball from the jar is

$\displaystyle \frac{2}{8} = \frac{1}{4}$

Thus, the probability of drawing red or yellow colored ball is

$\displaystyle 1 - \frac{1}{4} = \frac{3}{4}$