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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 doesnt 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, lets 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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