7a: Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events.

Students should start by developing a uniform probability model. In other words, have them start by identifying all the possible outcomes in the sample space and assigning them each an equal probability. (It helps to remind them that the sum of their probabilities in the sample space needs to be 1.) Once they've done that, they can add the probabilities of all the individual outcomes that make up their event to find the probability.

For example, say you put one garden snake, one ball python, and one rattlesnake in a bag and ask students to calculate the probability of choosing the rattlesnake. We can start by assuming that (1) you're crazy, and (2) we have an equal probability of choosing each type of snake. Since we've got three outcomes in our sample space (garden snake, ball python, and rattlesnake), we can split up the total probability (a.k.a. 1) evenly into those three different outcomes.

That gives us a ; probability of choosing a garden snake, a ; probability of choosing a ball python, and a ; probability of choosing the rattlesnake. Students should understand that this works because the sum of the probabilities of all the outcomes in our sample space is . And preso! Without realizing it, we've found the probability of choosing the rattlesnake: .

That's the process we're talking about—assigning equal probabilities to outcomes and using that to solve probability problems. Don't be shy about asking for events that make up more than one outcome, either! Just the same, the probability of choosing a garden snake or a ball python is .

See? Not too bad—assuming we didn't choose the rattlesnake, that is.