MATH 1324 Quiz 6 Show all work in the space provided. Credit will be given only for work that is clear and readable. Please staple all pages together before turning in the quiz. 23. Give all answers as decimals correct to 4 significant decimal digits. A company advertises that its new toothpaste will prevent tartar buildup. It claims that 40% of people will have less tartar after three months of using the toothpaste. To justify the claim a clinical experiment is run with 20 people using the toothpaste for three months. Find the probability that a) only 4 of the twenty will have less tartar. a) ___________________ b) at least 4 of the twenty will have less tartar. b) ___________________ 24. A new drug claims that it is 85% effective when used to treat patients that have a terrible infection so all such patients with the infection at a local hospital are treated with this new drug. About 5% of the patients in a local hospital have this terrible infection. Give all answers as decimals correct to 4 significant decimal digits. a) What is the probability that a person hospitalized for this terrible infection is cured given treatment by this new drug? a) ___________________ b) What is the probability that a person recently released from this hospital was treated and cured of this terrible infection by this new drug? b) ___________________ c) If 20 people recently released from this hospital are surveyed, what is the probability that 2 of them were treated and cured of this terrible infection? c) ___________________ 25. Three cards are drawn from a standard deck. Write probabilities as reduced fractions. a) How many 3-card hands are possible? b) What is the probability that all three cards are diamonds? c) What is the probability that all three cards are in the same suit? d) What is the probability that all three cards are face cards? e) What is the probability of three of a kind? f) What is the probability of having a pair (exactly 2 of a kind)? g) What is the probability of having (exactly) 2 cards of the same suit? a) _____________ b) _____________ c) _____________ d) _____________ e) _____________ f) _____________ g) _____________ 26. You draw one card from a standard deck of playing cards. If you pick a heart, you will win $10. If you pick a face card, which is not a heart, you win $8. If you pick any other card, you lose $6. Do you want to play? a heart a face card not a heart any other card x p Probabilities must be exact fractions and not decimal numbers. 27. At Tucson Raceway Park, your horse, Soon-to-be-Glue, has odds of 19:1 against coming in first place, odds of 9:1 against coming in second place, and odds of 3:1 against coming in third place. First place pays $4,500 to the winner, second place $3,500 and third place $1,500. Is it worthwhile to enter the race if it costs $1,000? Be careful here -- you were given odds against and not probabilities! first place second place third place x p Probabilities must be exact fractions and not decimal numbers. 28. A construction company has just received a building contract. From past experience, the company estimates there is a 55% chance of making a $500,000 profit, a 8% chance of breaking even, and a 37% chance of losing $200,000, depending on weather conditions and other factors. What is the expected value of the company's contract