Common Core Standards: Math
4. Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value. For example, find a current data distribution on the number of TV sets per household in the United States, and calculate the number of sets per household. How many TV sets would you expect to find in 100 randomly selected households?
Students should be able to work backwards to figure out how empirical data will help them make approximations about samples and populations. Now, we're working with empirical (as in real) data and not theoretical data. That means it's time for the real world.
In the actual real world, outside of the cameras of reality TV, we may have problems where theoretical probabilities don't exist. Students must use sample data to arrive at their own actual probabilities, find expect values, and so on. That means knowledge of the equations P(X = a) = nCa • pa • qn – a and E(x) = x1p1 + x2p2 + … + xipi.
The best way to demonstrate this to students is to give them data (and lots of it), and have them figure out and calculate probabilities based on observation. They should also find expected values and calculated potential payoffs if necessary. This data can be made by you or simply searched for online to find actual scientific empirical data.
Students usually find real scientific data somewhat boring, so anything to do with making money (casinos, gambling, or the lottery) will usually spark the students' interest more than genetic sequencing of fruit flies. If you're determined to use those fruit flies, consider making them tap dance or something.