Skill: Compare probabilities

To compare the likelihood of two events:

1. Find the probability of each event.
2. Write each probability as a fraction:

$$\text{Probability}=\frac{\text{number of favorable outcomes}}{\text{total number of equally likely outcomes}}$$

3. Compare the fractions. The larger fraction represents the more likely event. Equal fractions mean the events are equally likely.

Example: A bag has 10 equally likely marbles:

• 4 red marbles
• 3 blue marbles
• 3 green marbles

Which is more likely: drawing a red marble or a blue marble?

Step 1: Find each probability.

There are 4 red marbles out of 10:

$$P(\text{red})=\frac{4}{10}$$

There are 3 blue marbles out of 10:

$$P(\text{blue})=\frac{3}{10}$$

Step 2: Compare the probabilities.

The fractions have the same denominator, so compare their numerators:

$$4>3$$

Therefore,

$$\frac{4}{10}>\frac{3}{10}$$

Answer: Drawing a red marble is more likely than drawing a blue marble.