Practise/Assesment Masters Answers

Practice/Assessment Masters Answers CHAPTER 6 Introduction to Probability

6.1 Basic Probability Concepts 6. 23% 1. a) certainty 7. a) No; odds and probability are different b) impossible measures. c) 50% likely 2h 2h 2P(A) = , P(B) = 1 1 1 h  k 2h  k 2. a) b) c) 2 4 13 b) P(A) = P(B) = 0 3 1 d) e) 13 26 6.3 Probability Using Counting 3. G G B Techniques G G 1 5 B 1. a) b) B 6 18 G G 1 1 B c) d) 6 12 B B G B 1 1 3 7 1 2. 4. a) b) c) d) 3 8 8 8 8 37 16 e) Answers may vary, for example, no twins or 3. a) 1 b) c) triplets on third pregnancy. 39 65 5. a) 0.6 7 1 4. a) b) b) No, sample size is too small. 9 36 c) Conduct many more trials. 2 13 6. a) Answers may vary. 5. a) b) b) Answers may vary, for example, 0.9. 15 15 c) Answers may vary, for example, 0.9. 1 3 4 d) Answers may vary. 6. a) b) c) 7. Answers may vary. 5 5 5 17 2 1 8. 7. a) b) 18 9 20 c) Answers may vary, for example, the company 2 9. is equally likely to send each CD, and will 3 not send the same CD in the second month 7 as the one sent in the first month. 10. a) B; P(B) = > 0.5 5 1 13 8. a) b) b), c) Answers may vary. 12 84

6.2 Odds 6.4 Dependent and Independent Events 1. a) 1:5 b) 1:5 1. a, c, and f are independent events; c) 1:11 d) 5:1 b, d, and e are dependent events 2. a) 2:3 b) 3:2 4 1 2. a) b) 3. a) 1:12 b) 1:3 663 221 c) 1:25 d) 3:23 2 2 4. a) 5:7 b) 3:1 c) d) 5. a) 1:3 b) 3:1 663 221 c) 0.4 d) 0.25

Copyright © 2003 McGraw-Hill Ryerson Limited Chapter 6 Answers  MHR 75 1 1 d) Answers may vary, for example, the pattern 3. a) b) remains consistent over the season. 169 169 0.75 0.25 1 3 4. a) 0.5 0.5 b) c) d) 0.35 0.65 338 338   4. 49:275 c) i) McGill 55%, deBrasco 45% ii) McGill 57%, deBrasco 43% 1 5. a) 0 b) iii) McGill 58.2%, deBrasco 41.8% 6 d) 0.583 0.417 ; McGill’s long-term market 1 15 6. a) b) share will be 58.3% and deBrasco’s will be 28 28 41.7%. 7. a) 66% b) 1.9 e) Answers may vary, for example, that these 8. 5 trends continue.

6.5 Mutually Exclusive Events Study Master, Chapter 6 5 1 1 7 1. a, and e are mutually exclusive; b, c, d, and f are 1. a) b) c) d) non-mutually exclusive 36 6 2 36 2 7 3 5 1 2 1 2 2. a) b) c) d) 2. a) b) c) d) 13 26 26 26 2 3 6 3 7 6 3. Answers may vary, for example, 3. a) b) 13 13 a) 0.5 b) 0.01 c) 0.99 4. a) 4. a) 1:12 b) 3:23 c) 3:10 S 5. a) 4:1 b) subjective TW SW 6. 5.3% 25 30 19 1 7. 11 17 576 21 17 1 1 8. a) b) 15 60 10 9. a) 6.4% b) 78.4% F 10. a) A and B equally likely; P(A) = P(B) = 0.000 46 11 34 79 32 b) A is still more likely; b) i) ii) iii) iv) P(A) = 0.000 46, P(B) = 0.000 17 138 69 138 69 1 41 11. a) v) 6 46 S 5. a) 0.87 b) 0.015 2 8 c) A female has a 50% chance of being selected. 1 5 36 36 1

6.6 Applying Matrices to Probability 6 5 Problems b) 1. b); the elements do not add to 1. 9 c): it is not a row matrix. S 2. a); there is a negative entry. <4 even b); the third row does not total 1. 1 1 17 36 c); it is not square. 18 36 d); the rows do not total 1. 17 1

3. a) lost 36 6 b) i) 0.45 ii) 51.75% iii) 52.9% c) 0.529

76 MHR  Chapter 6 Answers Copyright © 2003 McGraw-Hill Ryerson Limited 7 0.67 0.33 c) 9. a) 0.55 0.45 b) 18  0.3 0.7  S 7 11 doubles c) S(1) =0.5 0.5, S(2) = 0.48 0.52 ; 1 1 They show the respective likelihood that a 1 6 18 6 customer will visit F-Stop or Zoom’In on

their second and third visits. d) Zoom’In; steady state vector is 11 d) 0.47 0.53 18 e) Answers may vary, for example, market S Perfect trends will continue. Primes Squares 10. a), b) 5 7 8 12 36 27 E 4 4 2 13 E 12. a) b) c) 27C 9 9 18 E 4 13. a) A, and B could be transition matrices. E b) B will reach a steady state. C 272 0.3 0.7 C 14. a) 1 0 b) P =   27 0.6 0.4 4 c) i) 0.3 ii) 0.51 E 27 d) 0.46 0.54; long-term probability that E 2 Bucky will turn right or left, respectively. C C 27 E Alternative Test, Chapter1 6 C C 1 1 7 27 1. a) b) c) 5 2 10 c) 1; Yes, the sum of the probabilities for all 7 1 possible outcomes must equal 1. 2. a) b) 19 6 20 2 d) e) f) 2:1 c) Answers may vary, for example, the 27 27 1 empirical probability does not equal . 2 d) statistical fluctuation e) Conduct many more trials. 3. 343:657 4. a) Ally; her odds in favour are greater. b) P(C) = 0.1, P(A) = 0.105 1 7 7 5. a) b) c) 6 282 3 067 878 1 6. 6 7. a) 0.012 b) 0.0028 c) 0.52 d) 0.94 2 1 8. a) b) 5 20