Assignment 2 Model Answers STA1DCT 1. For regions with a larger population, it would be reasonable to expect more people becoming ill and therefore a greater need for more emergency departments. Therefore, population size could understandably explain this correlation. 2. (a) 4/52 = 1/13. (b) i. 0, 1,2, ... , 10. ii. (1/13) × 10 = 10/13. iii. 2/10 = 1/5. iv. 1/13. 3. (a) 36. (b) 1/36. (c) Simple events in A are (1,1), (1,2), (1,3), (2, 1), (2,2), (3, 1) (numbering 6 simple events). So P(A) = 6/36 = 1/6. (d) P(AC) = 1 - 1/6 = 5/6. (e) There are 11 simple events given as (2,1), (2,2), ... , (2,6) and (1,2), (3,2), (4,2), (5,2), (6,2). So P(B)=11/36. (f) No since they can both occur at the same time (i.e. (2,1) is one example). (g) i. The events in both A and B are (1,2), (2, 1), (2, 2) so the probability of both is 3/36 = 1/12. ii. There are 6 simple events in A and 11 in B. Three are in both so the total number of simply events in A or B is 6 + 11 - 3 = 14 so probability of A or B is 14/36 = 7/18. (h) 1 - 7/18 = 11/18.