hw3sol.pdf - MGT 201 Quantitative Analysis Homework 3 1(a Given that the outcome of the red die is 4 5 or 6(three equally likely outcomes having less

hw3sol.pdf - MGT 201 Quantitative Analysis Homework 3 1(a...

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MGT 201 - Quantitative Analysis Homework 3 1. (a) Given that the outcome of the red die is 4, 5 or 6 (three equally likely outcomes), having less than 5 means having a 4, so P ( B | A ) = 1 / 3 = 33 . 3% . (b) No: A and B do overlap (outcome 4 is contained in both A and B ). (c) Let’s calculate P ( B ) = P (1 or 2 or 3 or 4) = 4 / 6 = 2 / 3 = 66 . 7% 6 = P ( B | A ) . Therefore, A and B are not independent. (d) There are 36 equally likely outcomes for the result (blue die, red die): { (1,1), (1,2), . . . , (6,5), (6,6) } . Out of those, 6 correspond to event C : { (1,1), . . . , (6,6) } . Therefore, P ( C ) = 6 / 36 = 1 / 6 = 16 . 7%. (e) Given that D occurs, there are 6 equally likely outcomes for the result (blue die, red die): { (1,1), (2,1), . . . , (6,1) } . Only one of those 6 corresponds to event C : (1,1). Therefore, P ( C | D ) = 1 / 6 = 16 . 7%. (f) We have already found that P ( C ) = P ( C | D ) = 1 / 6 = 16 . 7%. Therefore, C and D are independent. (g) Given that D occurs, there are 6 equally likely outcomes for the result (blue die, red die): { (1,1), (2,1), . . . , (6,1) } . Only one of those 6 corresponds to event E : (2,1). Therefore, P ( E | D ) = 1 / 6 = 16 . 7%. 2. Denote R the event: resident supports raising the debt ceiling; N the event: resident does
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