Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.

Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.

Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value.

Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value.

Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.

Find the expected payoff for a game of chance.

Evaluate and compare strategies on the basis of expected values.

Use probabilities to make fair decisions.

Analyze decisions and strategies using probability concepts.