4.6 ODDS AND MATHEMATICAL EXPECTATION Mathematical Expectation: 1st HALF 1) A large company is considering opening two new factories in different towns. If it is opens in 4 Wilmington, it can expect to make $67,000 profit per year with a probability of . However, if it opens 7 3 in Middletown, it can expect to make a profit of $71,000 with a probability of only . What is the 7 company’s mathematical expectation? 2) A contractor is bidding on a road construction job that promises a profit of $210,000 with a probability of 7 and a loss, due to strikes, weather conditions, late arrival of building materials, and so on, of $46,000 10 3 with a probability of . What is the contractor’s mathematical expectation? 10 3) Mark Stanford is in a gambling casino that charges $2 per chance to roll an honest die. He will be paid, in dollars, the number of dots on the face of the die. Find his mathematical expectation. 4) Pete Sutherland selects one card from a deck of 52 cards. If it is an ace, he wins $5. If it is a club, he wins only $1. However, if it is the ace of clubs, then he wins an extra $10. What is his mathematical expectation? 5) Chris Kobus is a salesperson for Nike. He is analyzing his five best accounts and comes up with the following information: ACCOUNT WEEKLY SALES ESTIMATED PROBABILITY THAT SALES WILL BE REALIZED Lebron James 4698 0.61 Jordan 4203 0.82 Sharapova 4506 0.59 Tiger 4475 0.51 Miami Hurricanes 4388 0.46 Find the expected sales of each account. 4.6 ODDS AND MATHEMATICAL EXPECTATION nd 2 HALF ODDS IN FAVOR: ODDS AGAINST AN EVENT: 6) What are the odds in favor of the New York Mets winning the World Series if the probability of their 4 3 winning is and the probability of their losing is ? 7 7 - What are the odds against the Mets winning? 7) Yasik is in Bennigans. He decides to give the waiter a tip consisting of only 1 bill selected randomly from among the 6 that he has in his pocket. What are the odds against him giving the waiter a dollar tip if he has a dollar, a five dollar bill, a ten dollar bill, a twenty dollar bill, and a fifty dollar bill? 8) According to Orga’s Magazine for Math Students, 84% of seniors do not do their homework. a. If a senior is randomly selected what is the probability that the student does their homework? b. If a senior is randomly selected what are the odds in favor of the senior not doing their homework? c. If a senior is randomly selected what are the odds against the senior doing their homework? 9) According the Time magazine (Fall 1993, p. 14), 21% of all Los Angeles residents under 18 years of age are foreign born. If a Los Angeles resident under 18 years of age is randomly selected, what are the odds against the resident being foreign born? What are the odds in favor of the resident being foreign born?
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