SOLUTION: There is 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
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Question 1194761: There is 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 by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!
A = number of striped balls
A = 14-9+1 = 6
B = number of non-striped (aka solid-colored) balls
B = 8
The odds against getting a striped ball is B:A = 8:6 = 4:3 which is the final answer
When forming the odds against ratio, we list the number of things we don't want (the non-striped balls), a colon, then we list the number of things we do want (the striped balls). The ratio 8:6 reduces to 4:3 after dividing both parts by the GCF 2.
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If you wanted, you could think of it like this
A = number of successes
B = number of failures
B:A = odds against event A happening
On the flip side
A:B = odds in favor of event A happening
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