policy holders have no accident, 25% had one accident, and the remaining 15% had two or more accidents. Further, from their past 10 year history, the insurance company concludes that those who did not have any accident have a 1% chance of having an accident in the future, while those who had one accident have a 3% chance of having an accident in the future. Those who had two or more accidents in the past three years have 10% chances having an accident in the future. Suppose that shortly after the above study, one of their policy holders has an accident. What is the probability that this policy holder did not have any accident in the past three years?28 Suppose that in a bolt manufacturing plant, machines A, B, and C manufacture, respectively, 45%, 25%, and 30% of the bolts. It is observed that the three machines produce, respectively, 5%, 2%, and 3% defective bolts. If the bolts produced by these machines are mixed in a well‐mixed lot and then a randomly selected bolt is found to be defective, find the probability that the defective bolt is produced by (a) machine A, (b) machine B, and (c) machine C.
29 A poll was conducted among 1000 registered voters in a metropolitan area asking their position on bringing a casino in that city. The results of the poll are shown in the following table:SexPercentage ofPercentagePercentage notPercentagevoters polledfavoring casinofavoring casinohaving no opinionMale55%75%20%5%Female45%40%50%10%What is the probability that a registered voter selected at randomWas a man, given that the voter favored the casino?Was a woman, given that the voter has no opinion about the casino?Was a woman, given that the voter did not favor the bringing in of a casino?
30 Let a random variable be distributed as shown below.01234560.10.090.20.150.160.2Find the probability .Find the probability .Find the probability .Find the probability .
31 Determine which of the following distributions do not represent a probability distribution. Justify your answer.(a)0123450.10.090.20.150.160.2(b)012345−0.10.090.30.150.160.4(c)0123450.20.090.20.150.160.2
32 In Problem 31, construct a bar chart for the probability distribution that satisfies the conditions of a probability distribution.
33 The following Venn diagram describes the sample space S of a random experiment and events A, B, and C associated with the experiment. (S consists of 12 elements, denoted by )Express the events A, B, and C in terms of the elements .Suppose that the sample points in the sample space S are equally likely.Find the following probabilities:
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