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##### Learning Outcome Statements
 1. Introductiondefine a random variable, an outcome, and an event; identify the two defining properties of probability, including mutually exclusive and exhaustive events, and compare and contrast empirical, subjective, and priori probabilities; describe the probability of an event in terms of odds for and against the event; 2. Unconditional, Conditional, and Joint Probabilitiescalculate and interpret conditional probabilities; 3. Addition Rule for Probabilities: the Probability that at Least One of Two Events Will Occurdemonstrate the application of the multiplication and addition rules for probability; 4. Multiplication Rule for Independent Eventscompare and contrast dependent and independent events; 5. The Total Probability Rulecalculate and interpret an unconditional probability using the total probability rule; 6. Expected Value (Mean), Variance, and Conditional Measures of Expected Value and Variancecalculate and interpret the expected value, variance, and standard deviation of random variables; explain the use of conditional expectation in investment applications; interpret a probability tree and demonstrate its application to investment problems; 7. Expected Value, Variance, Standard Deviation, Covariances, and Correlations of Portfolio Returnscalculate and interpret the expected value, variance, standard deviation, covariances, and correlations of portfolio returns; 8. Covariance Given a Joint Probability Functioncalculate and interpret the covariances of portfolio returns using the joint probability function; 9. Bayes' Formulacalculate and interpret an updated probability using Bayes' formula; 10. Principles of Countingidentify the most appropriate method to solve a particular counting problem and analyze counting problems using factorial, combination, and permutation concepts.
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