Math 13 Exam#3 May 22, 2012 SHOW ALL YOUR WORK!! Name: 1. Purchasing a home. Esther and Marcello have just purchased a home for $420, 000. They obtained financing with the following terms: a 20% down payment and the balance to be amortized over 30 years at 4%. (a) What is their down payment? (b) What is the loan amount? (c) How much is their monthly payment on the loan? (d) How much total interest (total amount paid - loan amount) do they pay over the life of the loan? (e) What is the loan balance, after they have made payments for 20 years? (f) If they pay an additional $200 each month toward the loan (starting with the first payment), when would the loan be paid off (round to the nearest month)?
2. Let the universal set, U = {a, b, c, d, e, f, g, h}, X = {a, c, e, h}, and Y = {a, b, d, g}. Find the set X Y. X Y = { 3. Let A and B be two events of a sample space S. If P (A) = 0.55, and P (B) = 0.25, and P (A B) = 0.65, find each of the following probabilities: (a) P (A B) (b) P (A B) (c) P (B) (d) P (A B) Page 2
4. In a survey of 75 business travelers, it was found that of three daily newspapers, New York Times, Wall Street Journal, and USA Today 23 read New York Times 18 read Wall Street Journal 14 read USA Today 10 read New York Times and Wall Street Journal 9 read New York Times and USA Today 8 read Wall Street Journal and USA Today 5 read all three Use a Venn Diagram to find out (a) How many of these business travelers read none of these newspapers. (b) How many of these business travelers read New York Times alone. (c) How many of these business travelers read neither New York Times nor Wall Street Journal? Page 3
5. Sean is making a sandwich with one type of meat, one slice of cheese, a condiment, and a slice of bread. He has turkey, roast beef and ham as meat choices, gouda, pepper jack, provolone, and cheddar cheese, and for condiments, mayo and mustard? In addition, he has rye, whole wheat, or french bread. How many different types of sandwiches could he make? 6. According to an insurance company, the probability that a man will survive one year is 0.991 and the probability that he will die one year is 0.009. A life insurance pays out a premium to whomever is listed as that person s beneficiary (spouse, child etc) should he/she pass away. If a man buys a $20, 000 premium one-year term life insurance policy for $210, what is the insurance company s expected gain or loss? Page 4
7. Suppose a family can choose between 100 names to name their newborn child. (a) In how many ways can the child be named if he/she will be given 3 (different) names? (b) In how many ways can the child be named if he/she will be given 1, 2, or 3 (different) names? 8. A recent poll of residents in a certain community revealed the following information about voting preference. Democrat Republican Independent Male 50 40 30 Female 60 30 25 (a) What is the probability that a resident votes Democrat? (b) What is the probability that a female resident votes Democrat? Page 5
9. Five cards are dealt from a standard deck of 52 cards. What the probability that (a) all cards are hearts? (b) at least one of the cards is a queen? (c) the first two cards are aces and last three are jacks? 10. EXTRA CREDIT!! A coin is tossed until, for the first time, either two heads or two tails appear in succession. What is the probability that the experiment will end before the sixth toss? Page 6