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# HW2 - Section 2.4 2.5 Probability(p.55 2.54 Suppose that in...

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Section 2.4 - 2.5 Probability (p.55) 2.54 Suppose that in a senior college class of 500 students it is found that 210 smoke, 258 drink alcoholic beverage, 216 eat between meals, 122 smoke and drink alcoholic beverages, 83 eat between meals and drink alcoholic beverages, 97 smoke and eat between meals, and 52 engage in all three of these bad health practices. If a member of this senior class is selected at random, find the prob- ability that the student (a) smokes but does not drink alcoholic beverages; sol) Let A be the event that students smoke, B be the event that students drink alcoholic beverage, and C be the event that students eat between meals. P ( A B 0 ) = P ( A ) - P ( A B ) = 210 500 - 122 500 = 88 500 (b) eats between meals and drinks alcoholic beverages but does not smoke; sol) P ( C B A 0 ) = P ( B C ) - P ( A B C ) = 83 500 - 52 500 = 31 500 (c) neither smokes nor eats between meals. sol) P (( A C ) 0 ) = 1 - P ( A C ) = 1 - 329 500 = 171 500 2.56 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 mutual funds with a probability of 0.3, and will invest in both tax-free bonds and mutual funds with a probability of 0.15. At this time, find the probability that a customer will invest (a) in either tax-free bond or mutual funds; sol) Let A be an event that a customer will invest in tax-free bonds and B be an event that a customer will invest in mutual funds. Then, P ( A ) = 0 . 6, P ( B ) = 0 . 3, and P ( A B ) = 0 . 15. P ( A B ) = P ( A ) + P ( B ) - P ( A B ) = 0 . 6 + 0 . 3 - 0 . 15 = 0 . 75 (b) in neither tax-free bonds nor mutual funds. sol) P (( A B ) 0 ) = 1 - P ( A B ) = 1 - 0 . 75 = 0 . 25 1

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2.60 A pair of fair dice is tossed. Find the probability of getting (a) a total of 8; sol) Let A be an event that getting a total of 8. A = { (2 , 6) , (3 , 5) , (4 , 4) , (5 , 3) , (6 , 2) } P ( A ) = 5 36 (b) at most a total of 5. sol) Let B be an event that getting at most of a total of 5. B = { (1 , 1) , (1 , 2) , (2 , 1) , (1 , 3) , (2 , 2) , (3 , 1) , (1 , 4) , (2 , 3) , (3 , 2) , (4 , 1) } P ( B ) = 10 36 = 5 18 2.62 If 3 books are picked at random from a shelf containing 5 novels, 3 books of poems, and a dictionary, what is the probability that (a) the dictionary is selected?
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