# Prize Winner, Part 1

### Resources for this lesson:

> Glossary

> Calculator Resources

> Teacher Resources: Instructional Notes

Are you ready to play? Let’s play Rock, Paper, Scissors! [Rock beats scissors; scissors beats paper; paper beats rock.] Get your fist ready. You can play up to 10 rounds.

## Check Your Understanding

Did you win? Lose? Tie?

What are the chances of winning Rock, Paper, Scissors? Will you improve your chances of winning if you always choose rock?

Show AnswerHide Answer

This tree diagram shows all possible outcomes
for the game Rock, Paper, Scissors. The win, lose and tie
would be from one player's point of view.
If you count the possibility of a tie, the probability
of winning is $\frac{3}{9}=\frac{1}{3}$. If you remove ending in a tie, then
the probability of winning is $\frac{3}{6}=\frac{1}{2}$.
If you always choose rock, and include the possibility of a tie, the probability
of winning is still $\frac{1}{3}$. If you remove the possibility of ending in a tie, then
the probability of winning is still $\frac{1}{2}$.
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Do you have your own strategy when playing this game? Is there a way to maximize the probability of winning this game? By the end of this module, you will be able to answer these questions.

When presented with a data set or situation, there are some general steps you can follow to solve the problem.

**Create and Analyze**– Look at the data. Find various ways to model the mathematics, such as with a graph, table or equation. Make sense of the problem you are working with by reasoning through concepts you already know that may help you solve the problem.**Test and Confirm**– Analyze the models and representations to develop strategies you think work best to solve the problem. You may need to try a few strategies and models until you get the one that is best. Persevere in solving the problem. Continually ask yourself if the steps you are following and what you are calculating make sense in the context of the problem. Don’t be afraid to change your strategy if necessary.**Apply the Model**– Employ your chosen models, representations and strategies. Input the necessary data, quantitative values, etc., and perform the necessary calculations with precision. Analyze the final results. Do they make sense in the context you have?