Understands and applies probability
Probability is the study of chance and likelihood. For example, the outcome of flipping a coin depends on chance. You don't know if you will get "heads" or "tails," but each is equally likely so we say the probability of getting heads is ½, which means that if you (fairly) flipped a (fair) coin many times you would get heads about half the time.
The study of probability should include the essential ideas needed for inferential statistics. Experiments should be conducted to give the idea of sample space and events. Counting techniques, including permutations and combinations, should be applied to probability. The probability of an event, when the outcomes are equally likely, should be understood as the ratio between the size of the event (number of favorable outcomes) and the size of the sample space (number of possible outcomes).
The rules of the probability of events and compound events should be addressed in terms of the students' experiments and simulations. Special emphasis should be given to the addition rule, because of the need to consider the intersection, the analysis of which leads to the ideas of independent, dependent, multiplication rule, mutually exclusive, and conditional probability.
The notion of random variables (possible numerical outcomes) and probability distribution of a discrete random variable should be introduced through simple experiments. Students should compare and contrast the experimental and theoretical probabilities of the distribution. The analysis of the probability distribution should include the expected value and measures of variability. Various types of probability distributions (binomial, geometric, normal) should be studied.