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Chapter 15

Chapter 15.docx

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Mahinda Samarakoon

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Stats: Data and Models – Canadian Edition Chapter 15 – Probability Rules Conditional Probability – It depends… - Conditional probability – probability that takes into account a given condition - When we want the probability of an event from a conditional distribution, we write P(B|A) and say “the probability of B given A” o P(B|A) = P(A and B)/P(A) - The formula does not work if P(A) = 0 Independence C - Dependent events – P(B|A) ≠ P(B|A ), the probability of B is not the same conditional on A as it is conditional on A C - Independent events - P(B|A) = P(B|A ) = P(B), the probability of B is the same conditional on A as it is conditional on AC - Events A and B are independent if and only if the probability of B is the same when we are given that A has occurred – P(B) = P(B|A) The General Multiplication Rule - P(A and B) = P(A) x P(B|A) - The probability that two events, A and B both occur is the probability that A occurs multiplied by the probability that B occurs (given that A occurs) The Multiplication Rules for Independent Events - For two independent events A and B, the probability that both A and B occur is the product of the probabilities of the two events o P(A and B) = P(A) x P(B), provided that A and B are independent - Putting the Multiplication Rule for Independent Events to Work o The phrase “at least” is a tip-off to think about the complement – happening at least once is the complement of not happening Independent ≠ Disjoint - Bot
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