Question

There are a rack of 14 billiard balls. Balls numbered 1 through 8 are solid-colored. Balls numbered 9 through 14 contain stripes. If one ball is selected at random, determine the odds against it being striped.

Answer 1

The odds against selecting a striped billiard ball from a rack of 14, with balls 9 through 14 being striped, are 4 to 3, as there are 8 solid-colored balls and 6 striped balls.

Step-by-step explanation:

To determine the odds against selecting a striped billiard ball from a rack of 14, where balls numbered 9 through 14 are striped, we must first understand what is meant by 'odds against'. The 'odds against' an event is the ratio of the number of ways the event cannot happen to the number of ways the event can happen. In this case, the event is selecting a striped ball.

There are 6 striped balls (numbers 9 through 14). Therefore, there are 14 - 6 = 8 solid-colored balls. The number of ways not to draw a striped ball is the same as drawing a solid-colored ball, which is 8 ways.

The odds against drawing a striped ball are therefore the ratio of solid-colored balls to striped balls, which is 8 to 6, or simply reduced to 4 to 3. This can also be expressed as odds against = number of solid-colored balls : number of striped balls = 8 : 6 = 4 : 3.

Answer 2

3/7 / 42.8% chance

Step-by-step explanation:

There are 6 striped balls (9, 10, 11, 12, 13, 14) and 8 (1, 2, 3, 4, 5, 6, 7, 8) solid colored balls. So, 6 / 14 balls are striped.

(6 / 14 = 3 / 7)

this means that the probability of a ball being striped has the odds of 3/7

(3/7 = about 42.8% chance)