Chapter 7, Problem 24CP

To determine

To Find: The quantity of balls of a certain color in a bag, given the odds of picking it from a bag.

Answer to Problem 24CP

There are $4$ red balls in the bag

Explanation of Solution

Given Information:

• There are $12$ more green ball than there are red balls.
• The odds of selecting a red ball are $1:4$

Concept Used: The odds of picking a red ball is given by the ratio of the number of balls which are red and the number of balls which are not red. In this case, the balls which are not red are only the green balls.

Assume the number of red balls in the bag $=x$ .

Then, the number of non-red(green) balls in the bag $= x+12$

Since the odds of selecting a red ball from the bag is $1:4$ , write

  $\frac{x}{x+12}=\frac{1}{4}$

If two ratios are equal, their cross products must be equal. Therefore,

  $4\cdot x=1\cdot \left(x+12\right)$

  $\Rightarrow 4x = x+12$

Subtract $x$ from the equation to get

  $3x = 12$

Divide the equation by $3$ to get

  $\frac{3x}{3}=\frac{12}{3}$

  $\Rightarrow x=4$