5. The Total Probability Rule
h. calculate and interpret an unconditional probability using the total probability rule;
i. explain the use of conditional expectation in investment applications;
j. explain the use of a tree diagram to represent an investment problem;
What is the total probability rule and what is the mathematical notation?
When you add up the individual probabilities of all the mutually exclusive and exhaustive scenarios, it will equal one.
$$P(A) = P(A|S_1)P(S_1) + P(A|S_2)P(S_2) + ... + P(A|S_n)P(S_n)$$
In what case would you use the total probability rule?
You use this rule if you're given multiple scenarios, each with its own probability of happening, and you are asked to calculate the overall probability.