Question 31·Easy·Probability and Conditional Probability
A jar contains candies of three different colors, as shown in the table.
| Color | Number |
|---|---|
| Green | 12 |
| Yellow | 8 |
| Purple | 4 |
| Total | 24 |
If one candy is selected at random from the jar, what is the probability that the candy is not green?
For basic probability questions with tables, always: (1) translate the description into a clear "success" condition (here, any candy that is not green), (2) add the counts that satisfy that condition to get the favorable outcomes, (3) use the total from the table as the denominator, and (4) simplify the resulting fraction. Pay special attention to words like "not" or "at least" so you don’t accidentally count the wrong group.
Hints
Focus on what "not green" means
"Not green" includes all candies that are any color other than green. Which colors in the table count as not green?
Count the non-green candies
Add together the numbers of all the non-green colors to find how many candies are not green.
Form the probability
Probability is . Use the total from the table as the denominator.
Simplify your fraction
After you form the fraction, see if both the numerator and denominator can be divided by the same number to reduce it.
Desmos Guide
Enter the probability expression
In Desmos, type (8+4)/24 to represent the probability of selecting a candy that is yellow or purple out of 24 candies.
View and interpret the result
Look at the value Desmos gives for (8+4)/24, and, if needed, tap it to see the fraction form. That fraction is the probability that the candy is not green.
Step-by-step Explanation
Identify how many candies are not green
The jar has 3 colors:
- Green: 12
- Yellow: 8
- Purple: 4
"Not green" means yellow or purple. Add the yellow and purple candies:
- Non-green candies .
Write the probability as a fraction
Probability is
Here, the favorable outcomes are the non-green candies (12), and the total number of candies is 24, so the probability is .
Simplify the fraction
Simplify by dividing the numerator and denominator by their greatest common factor, 12:
So, the probability that a randomly selected candy is not green is .