Assign numerical values to each event in a sample space to define a random variable and graph its probability distribution. Calculate the expected value of this random variable and interpret it as the mean of its distribution. Develop a probability distribution for a random variable for which theoretical probabilities can be calculated; calculate its expected value. An example could be the theoretical probability distribution for guessing all answers on a four-choice multiple-choice test, and the expected grade using different grading methods.

Create a probability distribution for a random variable with empirically assigned probabilities and calculate its expected value. For instance, find a data distribution for the number of TVs per household in the US and calculate the expected number of TVs in 100 randomly selected houses. Calculate the expected payoff for games of chance, such as the expected winnings from a state lottery ticket or a fast food game.

Compare strategies based on their expected values, such as comparing different auto insurance policies using varied chances of having minor or major accidents. Use probabilities to make unbiased decisions using methods like a random number generator. Apply probability concepts to analyze decisions and strategies in scenarios like product testing, medical testing or pulling a hockey goalie at the end of a game.