Skill: Use probability to make decisions

Probability tells how likely an event is.

• $0$ or $0\%$ means impossible.
• $1$ or $100\%$ means certain.
• A probability between $0$ and $1$ means the event might happen, but it is not guaranteed.

For equally likely outcomes, use:

$$P(\text{event})=\frac{\text{number of favorable outcomes}}{\text{total number of outcomes}}$$

To make a decision, find and compare the probabilities. Choose the option with the greater probability if you want the event to be more likely.

Example: You can choose one of two games. In each game, you win if you get blue.

• Game A: Pick one marble from a bag with $3$ blue marbles and $2$ red marbles.
• Game B: Spin a spinner divided into $8$ equal sections. $5$ sections are blue.

Which game should you choose to make winning more likely?

Step 1: Find the probability of winning Game A.

There are $3+2=5$ marbles total, and $3$ are blue.

$$P(\text{win Game A})=\frac{3}{5}=0.6=60\%$$

Step 2: Find the probability of winning Game B.

There are $8$ equal sections, and $5$ are blue.

$$P(\text{win Game B})=\frac{5}{8}=0.625=62.5\%$$

Step 3: Compare the probabilities.

$$62.5\%>60\%$$

Game B has the greater probability of winning, so Game B is the better choice if you want to make winning more likely.

Remember: Game B is more likely to win, but winning is not certain. You could still land on a non-blue section.