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Unformatted text preview: Chapter 7.5 Part Two: Independent Events • In many cases, knowing the outcome of one event does not provide any information for a second event, or affect the probability of the second event occurring. • For example, suppose we were to roll two dice, and were concerned with the events A , that the first roll is a five, and B , the second roll is a four. • Suppose I know that A has occurred. This doesn’t in any way change the likelihood that B will occur. Since the occurrences of A and B do not affect each other, we say that A and B are independent events . • Symbolically, we can express this as P ( B  A ) = P ( B ). • In some cases, it we can use our intuition to tell that events are in dependent. But we must be careful, because intuition can lead us astray! We need a way to test whether or not two events are indepen dent. The equation given above is maybe too difficult to work with. We will simplify it and come up with an easier test. • We know that if B and A are independent events, then P ( B  A ) = P ( B ). Now, let’s use our formula for conditional probability. We have the following: P ( B ∩ A ) P ( A ) = P ( B ) • Bringing the P ( A ) to the other side, we have P ( B ∩ A ) = P ( B ) P ( A )....
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 Spring '11
 stephenlang
 Calculus, Conditional Probability, Probability, Probability theory

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