**Unformatted text preview: **FDMAT 108 Unit 3 Practice Exam Key 4D -‐ c 1. Consider a typical 30-‐year fixed-‐rate mortgage. During which of the following years is the highest portion of each payment applied toward interest? a) 30th year b) 15th year c) 1st year d) 25th year 4D – a 2. Calculate the monthly payments for a home mortgage of $180,000 with a fixed APR of 4.5% for 30 years. a) $912.03 = 4D -‐ b b) !"#
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! !∗( $937.37 c) $2597.20 d) $886.69 .!"# = !"#,!!!∗( !" )
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!" 3. The following table shows the expenses and payments for 3 months on a credit card account with an initial balance of $500. Use a table similar to the one below as a guide to help you find the balance at the end of the three months. Assume that the interest rate is 1% per month (12% APR) and that the interest for a given month is charged on the balance from the previous month. Month Payment Expenses Interest Balance 0 $500 1 $120 $160 2 $35 $70 3 $70 $95 The final balance for month 3 is: a) $645.25 b) $616.30 c) $585.45 d) $545.30 Month Payment Expenses Interest Balance 0 $500 1 $120 $160 $5 $545 2 $35 $70 $5.45 $585.45 3 $70 $95 $5.85 $616.30 4D – c 4. Assume a home mortgage monthly payment is $760 and the balance on the 30-‐year loan is currently $135,250. Knowing that the mortgage is financed with 4.5% APR, what do you know about the principal and interest portions of this upcoming month’s payment? a) Interest = $335.20 and Principal = $424.80 b) Interest = $85.67 and Principal = $674.33 c) Interest = $507.19 and Principal = $252.81 d) Not knowing what month is being discussed, you cannot calculate this. Interest: 135,250 * .045/12 = 507.19 Principal: 760 – 507.19 = 252.81 4D -‐ c 5. Suppose that you have a balance of $2500 on your credit card, which charges an APR of 18% compounded monthly. If you want to pay off the balance in 30 months, how much should you pay each month instead of a minimum payment? (Assume that you make no additional charges to the card.) a) $37.68 = 4D -‐ d b) !"#
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$66.60 c) $104.10 d) $93.68 .!" = !"##∗( !" )
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!" =$104.10 6. Suppose you apply for a 5 year car loan in the amount of $27,000 with an APR of 8% compounded monthly. Your monthly payment is $547.46. Determine the total amount of interest you pay over the five years (rounded to the nearest dollar). a) $6,706 = b) !"#
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! !∗( $9,706 c) $5,453 d) $5,848 .!" = !"###∗( !" )
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!" =$547.46 Total Interest = Total Payments – Principal Total Interest = ($547.46 * 5 * 12) -‐ $27,000 = $32,847.60 -‐ $27,000 = $5847.60 4D – c 7. You would like to purchase a car and have calculated that the most you can afford to borrow on a vehicle loan is $100 per month over five years with an APR of 4.5%. You determine the maximum loan amount to be a)
$3,454 b) $4,362 c) $5,364 d) $7,532 = 4D – b !"#
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.!"# (!!"∗!) [!!(!! ) P = $5,363.94 !" 8. You are checking out refinancing possibilities for your home loan (a principal balance of about $200,000) and discussing the pros and cons of a 30-‐year mortgage at 3.25% compounded monthly versus a 15-‐year mortgage at 2.85% compounded monthly. You find that the difference in total interest (between the 30-‐year and the 15-‐
year mortgage) would be a)
about $85,206 b) about $67,327 c)
about $55,364 d) about $129,532 30-‐year loan interest: 870.41 * 12 * 30 – 200,000 = 313,347.60 – 200,000 = 113,347.60 in interest 15-‐year loan interest: 1366.78 * 12 * 15 – 200,000 = 246,020.40 – 200,000 = 46,020.40 in interest Difference: 113,347.60 – 46,020.40 = 67,327.20 7A – a 9. Given that P(E) = .25, what must be true about event E? a) The event E is unlikely. b) The event E is sure to happen. c) The event E is impossible. d) The event E is probable, but not sure to happen. 7A – a 10. A restaurant offers pizza with 3 types of crust, 5 different toppings, and in 4 different sizes. How many different single topping pizzas could be ordered? a) 60 b) 12 c) 45 d) 32 3 x 5 x 4 = 60 7A – a 11. Which of the following statements best represents the notion of theoretical probability? a)
On a multiple choice test, each question has 7 possible answers. If you make a random guess on the first question, what is the probability that you are correct? b)
Of the last 100 people who failed the lie detector test, 23 turned out to be telling the truth. What is the probability that the next person who fails the test is actually telling the truth? c)
Every week, Joe plays chess with his father. Of the last 50 games Joe has won 55% of the games. What is the probability that Joe will win the next game? d)
It may be just a feeling I’m having, but it sure looks like there is a low probability I’m going to get a passing score on my next math exam. 7A -‐ c 12. On a multiple choice test, each question has 4 possible answers. If you make a random guess on the first question, what is the probability that you are correct? a) P(A) = 4 b) 0 !"#$%& !" !"#$ ! !"# !""#$
!"!#$ !"#$%& !" !"#$!%&' c) !
! d) 1 ! = ! 7A -‐ c 13. Of 1768 people who came into a blood bank to give blood, 394 people had high blood pressure. Use the empirical method to estimate the probability that the next person who comes in to give blood will have high blood pressure. a) 0.27 b) 0.14 c) 0.22 d) 0.45 394/1768 = .22 7A – c 14. A bag contains 6 red marbles, 3 blue marbles, and 1 green marble. After shaking them up thoroughly, you randomly select two marbles from the bag without replacement. What is the probability of selecting two red marbles? a) 0.6 b) 1.2 c) 0.33 d) 0.36 P(selecting two red marbles) = ! !" ! ∗ = .33 ! 7A -‐ d 15. What is the probability of not rolling a number larger than 4 with a fair die? ! a) P(rolling a number > 4) = ! b) ! ! ! c) !"#$%& !" !"#$ ! !"# !""#$
!"!#$ !"#$%& !" !"#$!%&' ! d) ! ! ! ! ! ! ! ! ! ! = = P(not rolling number > 4) = 1 – P(A) = 1 -‐ = 7A – a 16. Choose an assorted package of donuts at random. The probability is .35 that it is chocolate and .20 that it is glazed. What is the probability that a randomly chosen donut is something other than chocolate or glazed? a) 0.45 1 -‐ .35 -‐ .20 = .45 7B – a b) 0.55 c) 0.35 d) 0.80 17. Twelve jurors are selected from a pool of twenty. Determine whether the events A and B are independent. Event A: The first person selected is a woman. Event B: The second person selected is a woman. a) 7B – b No b) Yes 18. Determine whether the events A and B are independent. Event A: A couple’s first child is a girl. Event B: The couple’s second child is a girl. a) 7B – b No b) Yes 19. Find the probability of correctly answering the first 3 questions on a multiple choice test if random guesses are made and each question has 6 possible answers. a) 0.0278 b) 0.0046 c) 0.1667 d) 0.5 Is this problem? AND EITHER/OR AT LEAST ONCE If it is AND, is it? DEPENDENT INDEPENDENT Formula: P(A and B) = P(A) x P(B) = 1/6 x 1/6 x 1/6 = 0.0046 7B –a 20. Find the probability of selecting all women for a seven-‐person jury from a pool of 10 men and 10 women. a) 0.00155 b) 0.24138 c) 0.11207 d) 0.46373 Is this problem? AND EITHER/OR AT LEAST ONCE If it is AND, is it? DEPENDENT INDEPENDENT Formula: P(A and B) = P(A) x P(B given A) = 10/20 x 9/19 x 8/18 x 7/17 x 6/16 x 5/15 x 4/14 = .00155 7B -‐ b 21. Find the probability of randomly selecting a boy or a non-‐soccer player from a sixth-‐grade class of 12 boys, 7 of whom play soccer, and 15 girls, 10 of whom play soccer. a) 0.37 b) 0.63 c) 0.55 d) 0.92 Is this problem? AND EITHER/OR AT LEAST ONCE If it is EITHER/OR, is it? NON-‐OVERLAPPING OVERLAPPING Formula: P(A or B) = P(A) + P(B) -‐ P(A and B) = 12/27 + 10/27 – 5/27 = .63 7B –a 22. Among the contestants in a competition are 36 women and 22 men. If 5 winners are randomly selected, what is the probability that they are all women? a) 0.08227 b) 0.06985 c) 0.09212 d) 0.08523 Is this problem? AND EITHER/OR AT LEAST ONCE If it is AND, is it? DEPENDENT INDEPENDENT Formula: P(A and B) = P(A) x P(B given A) = 36/58 x 35/57 x34/56 x 33/55 x 32/54 = .08227 7B -‐ b 23. Of the 43 people who answered “yes” to a question, 9 were male. Of the 41 people who answered “no” to the question, 7 were male. If one person is selected at random from the group, what is the probability that the person answered either “yes” or was male? a) 0.702 b) 0.595 c) 0.512 d) 0.190 Is this problem? AND EITHER/OR AT LEAST ONCE If it is EITHER/OR, is it? NON-‐OVERLAPPING OVERLAPPING Formula: P(A or B) = P(A) + P(B) -‐ P(A and B) = 43/84 + 16/84 – 9/84 = 50/84 = .595 7B – a 24. In one town, 39% of adults exercise three times per week or more. Find the probability that 5 adults selected at random from the town all exercise three times per week or more? a) 0.009 b) 4.14 c) 0.086 d) 0.39 Is this problem? AND EITHER/OR AT LEAST ONCE If it is AND, is it? DEPENDENT INDEPENDENT Formula: P(A and B) = P(A) x P(B) = .39 x .39 x .39 x .39 x .39 = 0.009 7B – a 25. In many board games, you are allowed another turn if you roll doubles (two of the same number). What is the probability this could happen to you two times in a row? a) 0.028 b) 0.17 c) 0.33 d) 0.005 Is this problem? AND EITHER/OR AT LEAST ONCE If it is AND, is it? DEPENDENT INDEPENDENT Formula: P(A and B) = P(A) x P(B) = 6/36 x 6/36 = .028 7B -‐ c 26. Find the probability of getting a sum of either 4 or 7 on a roll of two dice. a) 0.14 b) 0.11 c) 0.25 d) 0.28 Is this problem? AND EITHER/OR AT LEAST ONCE If it is EITHER/OR, is it? NON-‐OVERLAPPING OVERLAPPING Formula: P(A or B) = P(A) + P(B) P(sum of 4) = 1 + 3, 3 + 1, 2 + 2 = 3/36 P(sum of 7) = 3 + 4, 4 + 3, 2 + 5, 5 +2, 6 + 1, 1 + 6 = 6/36 3/36 + 6/36 = 9/36 = .25 7B -‐ d 27. A study conducted at a certain college shows that 60% of the school’s graduates find a job in their chosen field within a year after graduation. Find the probability that among 7 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduating. a) 0.600 b) 0.143 c) 0.972 d) 0.998 7C -‐ b Is this problem? AND EITHER/OR AT LEAST ONCE If it is AT LEAST ONCE: How many trials? 7 Formula: P(at least one event A in n trials) = 1 – [P(not event A in one trial)]n = 1 – .47 = .998 28. An insurance policy sells for $730. Based on past data, an average of 1 in 60 policyholders will file a $10,000 claim, an average of 1 in 120 policyholders will file a $20,000 claim, and an average of 1 in 300 policyholders will file a $50,000 claim. What is the expected value to the company per policy sold? a) $500 b) $230 c) $260 d) $255 Event Value Probability Value * Probability Sell Policy +$730 1 $730 x 1 = $730 !
1
Pay $10,000 claim -‐$10,000 -‐$10,000 * = −$166.67 !"
60 Pay $20,000 claim Pay $50,000 claim -‐$20,000 1 120 -‐$50,000 1 300 -‐$20,000 * -‐$50,000 * ! !"# !
!"" = -‐$166.67 = −$166.67 SUM: $229.99 7C -‐ b 29. Suppose a charitable organization decides to raise money by raffling a trip worth $500. If 3,000 tickets are sold at $1.00 each, find the expected value for a person who buys 1 ticket. a) -‐$0.85 b) -‐$0.83 c) -‐$0.81 d) -‐$1.00 Event Value Probability Value * Probability Buy raffle ticket -‐1 1 -‐$1 x 1 = $-‐1 !
1
Win raffle +500 +$500 * = .167 !"""
3000 SUM: $ -‐0.83 7C -‐ d 30. An insurance company sells an insurance policy for $1,000. If there is no claim on a policy, the company makes a profit of $1,000. If there is a claim on a policy, the company faces a large loss on that policy. The expected value to the company, per policy, is $250. Which of these statements is (are) true? A: The most likely outcome on any single policy is a profit for the company of $250. B: If the company sells only a few policies, its profit is hard to predict. C: If the company sells a large number of policies, the average profit per policy will be close to $250. a) 7C – b A and C b) B only c) C only d) B and C 31. For the students at one college the expected value for “number of siblings” is 3. Considering the Law of Large Numbers, which of the following statements is a reasonable conclusion? a)
If a student is selected at random, the most likely number of siblings for the student is 3. b)
If 100 students are selected at random, the average number of siblings for the 100 students will be close to 3. c)
If 4 students are selected at random, the average number of siblings for the 4 students will be 3. d)
If a student selected at random has 6 siblings, the next student selected will have no siblings. 7E – a 32. If you want to calculate the total number of outcomes where some items are selected from a set, each item may only be selected once, and the order of arrangement DOES matter, you would use the following formula: a) nPr b) nCr c) nr d) n! 7E -‐ b 33. If you want to calculate the total number of outcomes where some items are selected from a set, each item may only be selected once, and the order of arrangement DOES NOT matter, you would use the following formula: a) nPr b) c) nr d) n! nCr 7E – c 34. If you want to calculate the total number of outcomes where each item may be selected over and over, you would use the following formula: a) b) c) nr d) n! nPr nCr 7E – c 35. How many six character passwords consisting of lower case letters and numbers are possible if the last character must be a number? a) 452,390,400 b) 525,218,750 c) 604,661,760 d) 2,176,782,336 With repetition 36 x 36 x 36 x 36 x 36 x 10 = 604,661,760 7E – d 36. Imagine that you are judging the Junior Miss pageant and you need to select three winners (queen, first runner up, and second runner up) from 10 final candidates. How many outcomes are possible for these three winners? a) 6 ways b) 120 ways c) 210 ways d) 720 ways Without repetition, order important Permutations: nPr = 7E – a !! !!! ! 10P3 = !"! !"!! ! = 720 37. There are 13 members on a board of directors. If they must form a subcommittee of 4 members, how many different subcommittees are possible? a) 715 b) 17,160 c) 28,561 d) 52 Without repetition, order not important Combinations: nCr 13C4 = 715 7E – c 38. There are 5 women running in a race. If a person guesses randomly the first place, second place, and third place winners, what is the probability that they will guess all winners correctly? !
!
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a) b) c) d) !" !" Without repetition, order important Permutations: nPr = ! Probability of guessing all winners correctly = !" !" !"# !!
!!! ! 5P3 = !!
!!! ! = 60 7E – c 39. If the rules for the lottery game PowerBall required participants choose five unique numbers (ranging from 1 to 59) in any order along with one “powerball” (ranging from 1 to 35), what is the probability of winning the jackpot under these game rules? a) 1 in 5,153,633 b) 1 in 121,897,455 c) 1 in 175,223,510 d) 1 in 195,420,892 The total number of combinations of the 59 numbers chosen 5 at a time is 59C5 = 5,006,386 and we multiply this by the number of potential Powerball numbers (35) to get 175,223,510. 7E – b !"#! 40. Evaluate the following ratio by taking advantage of the definition of a factorial: !"#! a) 6 b) 331,373,196 c) 693 d) 479,556 ...

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