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Chapter 4, part D Download this file. Download this file.

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1 Chapter 4, part D Download this file. Download this file.

2 V. B. Independent Events Two events are independent if the fact that one has already occurred has no effect on the probability that the second will occur. P(A  B) = P(A) Example: Given Bill Clinton has a cat named “Socks” has no effect on the probability that another American will name their dog “Socks”.

3 Back to our example. Is marital status independent of age in the nightclub sample? If it is, P(S|U) = P(S) P(S|U) = P(S  U)/P(U) =.55/.65 =.846 P(S) =.75, so P(S|U)  P(S) This tells us that a person is more likely to be single, if we know they’re under 30, than any one random person is likely to be single with no information about their age.

4 C. The Multiplication Law This law is used to find the intersection of two events, P(A  B). Recall: P(A|B) = P(A  B)/P(B) Rewrite this and you have the multiplication law. P(A  B) = P(A|B)P(B), or P(A  B) = P(B|A)P(A)

5 Example of the multiplication law. Suppose a daily newspaper has the following subscription information: D= customer subscribes to the daily paper P(D)=.84 S= customer has the Sunday subscription. P(S|D)=.75 P(S  D) = P(S|D)P(D)=.75(.84) =.63 This means if you pick a customer out of their database the probability that they subscribe to both the daily and the Sunday papers is.63.

6 D. Mutually exclusive vs. Independent events Mutually exclusive events are those that don’t share any common sample points. P(A  B)=0 Independent events are those where the occurrence of one event has no effect on the probability of the other occurring. P(A  B) = P(A)

7 An example. Customers at a nightclub can either be under 21 (U) or over 21 years old (O). P(O)=.70P(U)=.30 These are mutually exclusive events; you can’t be in both sets! P(U  O)=0. But they are dependent events.

8 How does this work? Given that a person is over 21, what is the probability that they are under 21? Zero!!!! P(U|O) = P(U  O)/P(O) = 0/.70 = 0  P(U) =.30 Thus mutually exclusive events are necessarily dependent events because if you are in one set you are, by definition, precluded from being in the other set.


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