Common Core Standards: Math
7. Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.
If students don't know the important five-dollar words of probability yet, this is where they'll learn 'em. They're the same topics students have been talking about already, but with slightly more specific definitions:
- An outcome is the result of a single chance experiment.
- The sample space of an experiment is set of all possible outcomes of a single chance experiment.
- An event is a collection of outcomes.
Once they can talk the talk, they'll need to walk the walk. That means using this lingo to develop probability models to find probabilities of events—by which we mean coming up with a method to find probabilities.
Students should also realize that experimental and theoretical probabilities don't always see eye-to-eye, and they should know that it's okay. There are many reasons for this, a common one being that the number of trials might make a certain probability impossible. For example, if we flip a fair coin three times, there's never a way to have our experimental and theoretical probabilities match up; math won't allow it.
There's also the simple fact that chance processes are just it: chance. There's no guarantee that we'll get one of each number if we roll a die six times. If that were the case, it wouldn't be called probability; it'd be called certainty. Students should be able to understand and explain these sources of discrepancy, and not get bogged down by them. After all, life isn't perfect.
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