Exam review Questions

These questions you must be able to solve; order is random! Update Jan 8 2003

  1. Using matrix methods solve this system of equations
    2x - 5y +  7z =  4
    3x +   y - 12z = -8
    5x + 2y   - 4z =  3

    Ans; x = 1, y = 1, z = 1
  2. In how many ways can 9 students be evenly divided into three teams?
    Ans; 1680 (page 33 2.62)
  3. In how many ways can a committee consisting of 3 men and 2 women be chosen from 7 men and 5 women?
    Ans; 350
  4. How many distinct permutations can be formed from the letters in the word unusual?
    Ans; 840
  5. The probability that Jamie hits the target is ¼ and the probability that Alli hits it is 2/5. What is the probability that the target will be hit if Jamie and Alli each shoot at the target?
    Ans; 11/20 (page 58 4.9)
    1. How many ways can 3 boys and 2 girls sit in a row?
    2. In how many ways can they sit in a row if the boys and girls are to sit together?
    3. In how many ways can they sit in row if just the girls are to sit together?
    4. In how many ways can they sit in a ring?
    Ans; i) 120 (page 25 2.6) , ii) 24, iii) 48, iv) 24
  6. Find the steady state vector for this regular stochastic matrix
    ½    ¼    ¼
    ½    0    ½
    0    1    0
    Ans; 4/11,   4/11,   3/11 (page 139 7.14)
  7. Find the general term and the term containing x3, for the expansion (x2 + x-3)9
    Ans; C(9,k)(x2)9-k(x-3)k ; 84x3 (G page 217 #10)
  8. Find the 8th and 10th term of these series
    a) 15 + 45 + 135 + .....
    b) -8 + 4 - 2 + .....
    Ans; a) 32805, 295245 and b) 1/16, 1/64 (G Page 230 #2)
  9. Determine a and r for these geometric sequences given that
    a) t2 = 12 and t6 = 972
    b) t7 = -200 and t12 = 8/125
    Ans; a) a = 4 ; r = 3 and b) a =-312500 ; r = -0.2 (G page 230 #6)
  10. The mean deviation of a population is 42 and the standard deviation is 12. Find the measures in population that have the following z-scores
    a) 1.5 and b) -0.75
    Ans; a) 60 and b) 33 (G Page 340 # 3)
  11. The times that people wait in a grocery store checkoutline is normally distributed. The mean waiting time is 10 minutes with a 2.5 minute standard deviation. What is the probability that Jack will be through the checkoutline in less than 5 minutues?
    Ans; 0.0228 (G Page 350 # 9)
  12. A roullette wheel has 36 numbers on which a the ball can land. On any spin what is the probability that the ball will land on
    a) an even number, b) a prime number, c) a perfect square d) a multiple of 3
    Ans; a)1/2 , b) 1/3, c) 1/6, d) 1/3 (G 281 # 5)
  13. A man is dealt 5 cards one after another . What is the probability that they are all spades?
    Ans; 33/66640 (Page 61 4.8)
  14. A bin of fruit contains four apples and eight oranges. Five pieces of fruit are randomly chosen from the bin
    a) What is the probability that exactly three apples are chosen?
    b) What is the probability that all the pieces of fruit chosen are oranges?
    Ans; a) 0.1414 and b) 0.0707
  15. An urn containing 3 red marbles and 7 white marbles. A marble is drawn at random from the urn and a marble of the other colur is then put into the urn. A second marble is drawn from the urn.
    i) Find the probability p that the second marble is red.
    ii) If both marbles were the same colour, what is the probability p that they were both white
    Ans: start by drawing a tree diagram i) 17/50, ii) 7/8 This is a conditional probability question (Page 209 18.24 Finite Math)
  16. A student's study habits are as follows. If he studies one night, he is 70% sure of studying the next night. On the other hand, the probability that he does not study two nights in succession is 0.60. In the long run how often does he study? A Markov chain question. Set up a transition matrix
    Ans: 4/11 (Page 245 20.15 Finite Math)
  17. A tailor has 80 m2 of cotton material and 120 m2 of wool material. A suit requires 1.0 m2 of cotton and 3.0 m2 of wool and a dress requires 2.0 m2 of each. How many garments should the tailor make to maximze his income if
    i) a suit and dress each sells for $300
    ii) a suit sells for $300 and a dress for $200
    Before you start construct a table to summarize the facts. Each part has its own objective function.
    Ans: i) should make 20 suits and 30 dresses making $15 000 ii)
          ii) two possible answers; either 20 suits and 30 dresses or just 40 suits. (Page 315 24.13 Finite Math)
  18. Simplify and expand ((2x - y)4
    Ans: 16x4 -32x3y + 24x2y2 - 8xy3 + y4 (Page 147 13.10 Finite Math
  19. How many different signal flags, each consisting of 8 flags hung in a vertical line, can be formed from 4 red flags, 2 blue flags, and 2 green flags?
    Ans: 420 (Page 159 14.23 Finite Math) How would the ansswer change if the phrase "each consisting of 8 flags" was left out of the problems statement?
  20. Of 120 students 60 are studying French, 50 are studying Spanish, and 20 are studying French and Spanish. If a student is chossen at random, find the probability that the student
    i) is studying French or Spainish
    ii) is studying neither French nor Spanish
    Ans: i) 3/4, ii) 1/4 (Page 198 17.48 Finite Math)
  21. How many terms are there in this series?    1.5 + 3 + 6 + ..... + 3072 Ans; _____ (from a test)
  22. Determine the value of S for    6 + 2.4 + 0.96 + ......
    Ans; ______ (from old test)
  23. How many terms in the expansion (3x - 4y)17?
    Ans; _____ (from old test)
  24. What is the coefficient of the 4th term in the expansion (x2 - 4/x)8?
    Ans; -3584 (from old test)
  25. The all-pro AFC team has a roster of 3 quaterbacks and 8 wide-outs (recievers). If on any play the offensive coordinater has 1 quarterback and 3 wide-outs on the field at any given time, how many combinations of these players are possible?
    Ans; _____ (from old quiz)
  26. A bowl of mixed candies consists of 6 chocholates, 4 hard candies, 5 jube-jubes, and 3 toffees. If big Dave reaches in to pick some without looking, how many different selections might he make?
    Ans; 839 (from old quiz)
  27. Evaluate this sum: S8 = 3/16 + 3/4 + 3 + .....
    Ans; 4095.93 (from old quiz)
  28. Both the Blackhawks and Bulls are in action tonight. The probability that the Blackhawks win is 2/5 and the probability that the Bulls will is 3/7. Find the probability that i) both teams win tonight and ii) one of the teams win
    Ans; ________ (from old quiz)
  29. A game consists of drawing three cards from a deck of cards. If the first card drawn is a spade, you win $5.00, if the second card deawn is a spade you win $3.00, and if the third card drawn is a spade you win $2.00. If it costs you $2.50 to play this game, is this game reasonable fair? Must prove your answer.
    Ans; yes (from old quiz)
  30. A home made CD consists of three songs by Rare Earth and seven by Pink Flyod. If a CD player randomly selects three songs, what is the expected number of Rare Earth songs picked?
    Ans; 1.2 (from an old quiz)
  31. Jeff Garcia has attempted 549 passes during the regular season. He has completes 318 of them. In the first playoff game, what is the probability that
    i) he will complete his first pass on his second attempt ?
    ii) he will complete a pass on one or more of his first three attempts?
    Ans; i) 0.244,   ii) 0.9256 (from old quiz)
  32. Find the steady state vector for this matrix
      
    0.63   0.37
    0.24   0.76
    

    Ans; [0.3934   0.6066]
  33. Find n given that 7/4P(n-2,2) = C(n,4)
    Ans; ______ (old review sheet)
  34. 65% of families in our town own computers. 8 families are choosen at random.
    i) State the probability distribution function
    ii) What is the probability that at least 4 families own computers?
    ii) What is the expected number of families with computers?
    Ans; i) binomial distribution, ii) 0.894, iii) 5 families (from Allie)
  35. The mean and standard deviation on an exam are 74 and 12 respectively. Find the z-scores for students having marks i) 65 and ii) 86
    Ans; i) 0.75,   ii) 1.0 (Page 115 6.11 Probability)
  36. Let X be a random variable with a standard normal distribution. Find P(-1.37 ≤ X ≤ 2.01)
    Ans; 0.88925 ((Page 115 6.14 (iii) Probability)
  37. The life span of a particular species of turtle in captivity is normally distributed with a mean life span of 180 mo. and a standard deviation of 40 mo.
    a) Of 1000 turtles in captivity, approximately how many will live more than 220 mo.?
    b) What is the probability of a turtle living more than 100 mo.?
    Ans; a) 160,   b) 97.5%
  38. Given P(A) = 0.23     P(B) = 0.43     P(A ∩ B) = 0.15
    Find P(A U B)
    Ans; ____ (old test)
  39. If P(S | T) = 0.32     P(T | S) = 0.62 and P(S ∩ T) = 0.38
    Find P(S) and P(T)
    Ans; _____ (old test)
  40. A magazine poll sampling of 100 people gives the following results: 17 read magazine A, 18 read magazine B and 14 read magazine C.
    Also, 8 read magazines A & B,   7 read magazines A & C,   9 read magazines B & C and lastly 5 read all three magazines.
    i) Place the above information in a Venn diagram
    ii) How many people poled do not read any of the above magazines? iii) How many people read just one magazine ?
    Ans; ______ (old test)