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# Using Algebra in Statistics and Probability Study Guide (page 3)

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#### Example

The gumball machine contains 12 red gumballs, 8 green gumballs, 5 yellow gumballs, and 7 orange gumballs. How many green gumballs must be added to make the probability of selecting a green gumball ?

The probability of selecting a green gumball is equal to the number of green gumballs divided by the total number of gumballs. Let x represent the number of green gumballs added to the machine. That means there are now 8 + x green gumballs, and 12 + 8 + 5 + 7 + x = 32 + x total gumballs. The probability of selecting a green gumball is equal to . The value of x will make this probability equal to , so set the two fractions equal to each other and solve for x:

=

Cross multiply:

2(8 + x) = 32 + x
16 + 2x = 32 + x
16 + x = 32
x = 16

For the probability of selecting a green gumball to become , 16 green gumballs must be added to the gumball machine.

Find practice problems and solutions for these concepts at Using Algebra in Statistics and Probability Practice Questions.

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