Solving for the Probability of Selecting a White Candy

Imagine a scenario where you have three different colored candies: red, green, and white. The probability of selecting a red candy is 2/5 and the probability of selecting a green candy is 1/4. How can you determine the probability of selecting a white candy?

Understanding the Problem

In any scenario involving probabilities, the sum of all possible outcomes must equal 1. In this case, we need to determine the probability of selecting a white candy, given the probabilities of selecting a red and a green candy.

Setting Up the Equation

We start by defining the probabilities:

Let PRed represent the probability of selecting a red candy, which is 2/5. Let PGreen represent the probability of selecting a green candy, which is 1/4. Let PWhite represent the probability of selecting a white candy, which we need to solve for. The total probability of all outcomes must equal 1: PRed PGreen PWhite 1.

Applying the Total Probability Rule

Now, we can substitute the known probabilities into the equation:

PRed PGreen PWhite 1

Simplifying with the given values:

2/5 1/4 PWhite 1

Finding a Common Denominator

To solve for PWhite, we first need to convert the fractions to have a common denominator. The least common multiple (LCM) of 5 and 4 is 20. Let's convert the fractions:

2/5 8/20 1/4 5/20

Substituting these into the equation:

8/20 5/20 PWhite 1

Combining the fractions:

(8 5)/20 PWhite 1

13/20 PWhite 1

Solving for PWhite

Isolate PWhite by subtracting 13/20 from both sides:

PWhite 1 - 13/20

Convert 1 to a fraction with a denominator of 20:

PWhite 20/20 - 13/20

Subtract the numerators:

PWhite 7/20

Conclusion

The probability of selecting a white candy is 7/20.

Alternatively, if we assume the probability of selecting a red candy is 4/5 instead of 2/5, we can solve as follows:

PRed PGreen PWhite 1

4/5 1/4 PWhite 1

Convert 4/5 to a fraction with a denominator of 20:

16/20 5/20 PWhite 1

21/20 PWhite 1

Isolate PWhite by subtracting 21/20 from both sides:

PWhite 1 - 21/20

Convert 1 to a fraction with a denominator of 20:

PWhite 20/20 - 21/20

Subtract the numerators:

PWhite -1/20

This scenario is not possible, as probabilities cannot be negative.

Hence, the correct solution is: