STAT 3201 Lecture Notes - Lecture 6: Brown Hair, Conditional Probability
31 Jan 2017
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Document Summary
Conditional probabilities, independence, probability laws, and bayes theorem. A conditional probability for an event is calculated when we know additional information about the outcome of a random trial. Suppose a and b are two events for a random trial. Suppose also that it is known that b has already occurred. We can recalculate the probability of event a based on this new information. This is what"s called the conditional probability of a given b. P(a|b) is read probability of a given b . Example: suppose 200 randomly selected people were sent a survey, asking them their sex (male or female) and their hair color (black, brown, or blonde). The results of this survey are summarized in the following table: Two events are independent if the occurrence of one does not affect the probability that the other will also occur. The probability of the intersection of two events a and b is: p(a) p(b)
