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MTH 424/524 Homework 1




Question;1. Suppose that a number x is to be selected from the real line S, and let A, B, and C be the eventsrepresented by the following subsets of S, where the notion denote the set containing every point x forwhich the property presented following the colon is satisfied:.Describe each of the following events as a set of real numbers:(a)(b)(c)(d)(e)2. (a) How many three?digit numbers can be formed form the digits 0, 1, 2, 3, 4, 5, and 6, if each digitcan be used only once?(b) How many these are odd numbers?(c) How many are greater than 330?HW 113. In how many ways can 3 oaks, 4 pines, and 2 maples be arranged alone a property line if one doesnot distinguish among tree of the same kind?4. How many ways to arrange the letters ?s,s,s,t,t,t,i,i,a,c?? If the arrangement is random, what is theprobability that they spell the word ?statistics??5. From past experiences a stockbroker believes that under present economic conditions a customer will invest in tax?free bonds with a probability of 0.6, will invest in mutualFUNDS with a probability of 0.3,and will invest in both tax?free bonds and mutualFUNDS with probability of 0.15. At this time, find theprobability that a custom will invest(a) in either tax?free bonds or mutualFUNDS,(b) in neither tax?free bonds nor mutualFUNDS.6. Given,,, find(a)(b)2(c)3HW 17. Suppose that in a senior college class of 500 students it is found that 210 smoke, 258 drink alcoholicbeverages, 216 eat between meals, 122 smoke and drink alcoholic beverages, 83 eat between meals anddrink alcoholic beverages, 97 smoke and eat between meals, and 52 engage in all three of these badhealth practices. If a member of this senior class is selected at random, find the probability that student(a) smokes but does not drink alcoholic beverages,(b) eats between meals and drink alcoholic beverages but does not smoke,(c) neither smokes nor eats between meals.8. Tom thinks with probability 0.80 he will get ?A? in physics and with probability 0.60 he will get ?A?in chemistry. He also guesses that the chance he will get ?A? in both courses is 0.5. What is theprobability that Tom will get ?A? in exactly one of the two courses?


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