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By Pedroza C.

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D) Discuss the answer to (c) if n is large. 4. A shipment of 1500 washers contains 400 defective and IIOO nondefective items. Two-hundred washers are chosen at random (without replacement) and classified. (a) What is the probability that exactly 90 defective items are found? (b) What is the probability that at least 2 defective items are found? 5. Ten chips numbered I through 10 are mixed in a bowl. Two chips numbered (X, Y) are drawn from the bowl, successively and without replacement. What is the probability that X + Y 10?

5) yields the proportion of the entire amount of salt which is found in the ith beaker. The following illustration of Bayes' theorem will give us an opportunity to introduce the idea of a tree diagram, a rather useful device for analyzing certain problems. Suppose that a large number of containers of candy are made up of two types, say A B. Type A contains 70 percent sweet and 30 percent sour ones while B 'these percentages are reversed. Furthermore, suppose that 60 percent candy jars are of type A while the remainder are of type B.

The sample space is S = {O, 1, 2 }, where each outcome represents the number of heads that occur. -! This analysis is obviously incor­ EXAMPLE head appears}. In evaluating rect, since for the sample space considered above, all outcomes are not equally likely. In order to apply the above methods we should consider, instead, the sample space S' = {HH, HT, TH, IT}. -- We could use the sample space S correctly as follows: The outcomes 0 and 2 are equally likely, while the outcome I is twice as likely as either of the others.

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