# Prize Winner, Part 1

### Resources for this lesson:

Key Term

Conditional Probability

Again, you might be wondering what the difference is between the rule stating:

1. “What is the probability of a person selecting an even number and a multiple of five?”

versus:

2. “What is the probabilty of a person selecting a multiple of five, given that they selected an even number?”

A Venn Diagram makes this very clear.

Finding the probability of a person selecting an even number and a multiple of five means that we look at all the numbers 1 – 30, and select the numbers that are both even and a multiple of five. Three out of the thirty numbers fit this description, so the probability is $\frac{3}{30}=\frac{1}{10}$.
Finding the probabilty of a person selecting a multiple of five, given that they already selected an even number means that the person must begin with selecting the even number first. This limits us to just the fifteen even numbers. From that set, we then look for the multiples of five, which are 10, 20 and 30. Thus, the probabiltiy is $\frac{3}{15}=\frac{1}{5}$.