Chapter 11: Problem 1
In Exercises \(\mathrm{P} .1\) to \(\mathrm{P} .7,\) use the information that, for events \(\mathrm{A}\) and \(\mathrm{B},\) we have \(P(A)=0.4, P(B)=0.3,\) and \(P(A\) and \(B)=0.1.\) Find \(P(\operatorname{not} A)\),
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As in Exercise \(\mathrm{P} .35,\) we have a bag of peanut \(\mathrm{M} \& \mathrm{M}\) 's with \(80 \mathrm{M} \& \mathrm{Ms}\) in it, and there are 11 red ones, 12 orange ones, 20 blue ones, 11 green ones, 18 yellow ones, and 8 brown ones. They are mixed up so that each is equally likely to be selected if we pick one. (a) If we select one at random, what is the probability that it is yellow? (b) If we select one at random, what is the probability that it is not brown? (c) If we select one at random, what is the probability that it is blue or green? (d) If we select one at random, then put it back, mix them up well (so the selections are independent) and select another one, what is the probability that both the first and second ones are red? (e) If we select one, keep it, and then select a second one, what is the probability that the first one is yellow and the second one is blue?
Ask you to convert an area from one normal distribution to an equivalent area for a different normal distribution. Draw sketches of both normal distributions, find and label the endpoints, and shade the regions on both curves. The upper \(30 \%\) for a \(N(48,5)\) distribution converted to a standard normal distribution
Find endpoint(s) on the given normal density curve with the given property. \(\mathbf{P . 1 4 8}(\) a) The area to the left of the endpoint on a \(N(5,2)\) curve is about 0.10 (b) The area to the right of the endpoint on a \(N(500,25)\) curve is about 0.05
Class Year Suppose that undergraduate students at a university are equally divided between the four class years (first-year, sophomore, junior, senior) so that the probability of a randomly chosen student being in any one of the years is \(0.25 .\) If we randomly select four students, give the probability function for each value of the random variable \(X=\) the number of seniors in the four students.
Use the information that, for events \(\mathrm{A}\) and \(\mathrm{B}\), we have \(P(A)=0.8, P(B)=0.4\), and \(P(A\) and \(B)=0.25.\) Find \(P(\operatorname{not} B).\)
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