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There are two tasks in this activity. Task one relates to probabilities and probability distributions. Task two relates to data and statistics. Complete all parts of both tasks and arrange your responses in one professional$-$looking report, with all non$-$ILC sources cited accurately.

Your report may be a Word $(.$docx$)$ or PDF document, a slide show, or video with narration. In any form, the content should be written in a way appropriate for your peers.

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Create a random chance one$-$player game with prizes that is fun to play. The game should include all of the following elements:

The game should be fair. The expected value for the player should be $0.$ This could be accomplished by charging a set fee to play, or by adjusting prize amounts.

At least three different actions should be taken by the player while playing. Examples include, but are not limited to$,$ drawing a card, rolling a $12-$sided die, flipping a coin, etc.

For the game to be fun, the player should win $20-40\%$ of the time.

You must be able to play the game, or simulate playing it using online random number generators.

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You will submit the following items in the first part of your report.

A name for the game.

A description of the rules and instructions on how to play the game.

A photograph or diagram of any needed materials.

A distribution table for the prizes, and any calculations needed to justify the values.

The expected value of the game, with any supporting calculations.

Evidence that the player will theoretically win $20-40\%$ of the time.

The results of playing the game yourself $10$ times.

A comparison of the theoretical results of the game to your experimental results, including a discussion of whether your results were typical or rare.

Two constructive pieces of advice for another student working on this same task, explaining common errors that may be made in this task and ways to avoid them.

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