Conditional Probability, Total Probability Theorem and ... - Berlin Chen
Conditional Probability, Total Probability Theorem and ... - Berlin Chen
Conditional Probability, Total Probability Theorem and ... - Berlin Chen
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<strong>Conditional</strong> <strong>Probability</strong> (1/2)• <strong>Conditional</strong> probability provides us with a way to reasonabout the outcome of an experiment, based on partialinformation– Suppose that the outcome is within some given event B , wewish to quantify the likelihood that the outcome also belongssome other given eventA– Using a new probability law, we have the conditional probabilityof given , denoted by , which is defined as:A BPA B P A BA B PPBP • If B has zero probability, P A B is undefined• We can think of P A B as out of the total probability of theelements of B, the fraction that is assigned to possibleoutcomes that also belong to AAB<strong>Probability</strong>-<strong>Berlin</strong> <strong>Chen</strong> 2
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