Evidence of Understanding

**compare probabilities of different events occurring and describe their effect on each other**- categorize and justify if/when events are
**mutually exclusive**(when the probability of the events occurring simultaneously is 0),**dependent**(including both unions and intersections of sample spaces), or**independent**- analyze and relate the multiplication rule and addition rule to the sample space and relationship between events

- show that events are independent
*if and only if*the product of their probabilities is equal to the joint probability of the events occurring - articulate how one event affects a subsequent event (
**conditional probability**) when events are independent or dependent - explain how the correct probability formula describes a desired operation/analysis on the sample space

- categorize and justify if/when events are
**use probability to predict and evaluate outcomes and expected values of decisions**- determine which probability formula should be used to predict outcomes for a given context
- apply probability rules to a given context and interpret the meaning of the outcomes within that context
- (+) weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.

- calculate the expected payoff for a game of chance
*Example: find the expected winnings from a state lottery ticket or a game at a fast-food restaurant*

- use probability and outcome values to justify the
**fairness**of a particular system (and if necessary can make recommendations to make the system more fair) - evaluate and compare strategies using
**expected values***Example: compare a high-deductible versus a low-deductible automobile insurance policy using various, but reasonable, chances of having a minor or a major accident*

- explain whether a model is consistent with results from a data-generating process
*Example: a model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model?*

Develop conceptual understanding:

mutually exclusive, independent, dependent, multiplication rule, addition rule, conditional probability, fairness, expected valueSupporting terms to communicate:

if and only if, sample space, frequency, event space, complimentary, expected value, possible outcomes, simultaneous, union, intersection, permutation, combination, disjoint, compound