Skill: Compare probabilities informally

First, list all the equally likely outcomes. Then list the outcomes that support each event. Compare the number of supporting outcomes.

Example: A fair number cube has the numbers $1,2,3,4,5,$ and $6$. Which is more likely: rolling an even number or rolling a number greater than $4$?

Step 1: List the outcomes.

The possible outcomes are:

$$1,\ 2,\ 3,\ 4,\ 5,\ 6$$

Because the number cube is fair, each number is equally likely to be rolled.

Step 2: Find the outcomes for each event.

• An even number: $2,4,6$
  This event has 3 supporting outcomes.
• A number greater than $4$: $5,6$
  This event has 2 supporting outcomes.

Step 3: Compare the numbers of supporting outcomes.

Rolling an even number has more supporting outcomes than rolling a number greater than $4$.

So, rolling an even number is more likely.

Remember, more likely does not mean certain. You could still roll $1$, $3$, or $5$. An event with no supporting outcomes is impossible, and an event that includes every outcome is certain.