Common Core Standards: Math
6. Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).
Mirror, Mirror, on the wall,
Which is the fairest of them all?
One of the best uses for probability is to help us understand whether or not events are truly random. This way, we can ensure that there is no bias on the part of any individuals involved, no bias on the part of the device being used, and therefore a "clean" and "fair" decision is being made.
Students should know that we use dice, coins, random number generators, lots, and many other things in order to ensure fairness. Still, there will always be deviation (and those people who claim they can roll double sixes with two fair dice ten times in a row).
Students should understand the factors that make decisions fair and random and be able to identify when such decision-making methods are biased or skewed. Students should also know that fairness and randomness are not necessarily synonymous, depending on specific situations.
In the classroom these questions can be demonstrated, simulated, and answered with many different examples. Here are a few ideas you can do to demonstrate them. First, come up with an example or a decision that needs to be made, then propose ways by which it can be made.
Are the decisions fair from a probability standpoint? Let the students decide after numerous tries to ensure randomness. Are the decisions fair from a moral standpoint (for instance, randomly deciding who fails the class based on a coin toss)?
- Toss a fair die
- Drop a fair die
- Toss an unfair die (but don't tell them about it)
- Select a randomly chosen card from a "fresh" deck of 52
- Flip a coin
- Use lots or straws
- Use a spinning top
- Use a random number generator
Discuss the strengths and weaknesses, randomness or bias, fairness or unfairness of each method from a mathematical standpoint. Discuss methods to undermine or enhance the fairness of each method, and when such methods will be useful in making decisions.