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sol3 - CSE 21 Solutions Problem Set 3 1 Note for parts(b...

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CSE 21: Solutions - Problem Set 3 1. Note: for parts (b) and (c), the answers may vary from student to student due to randomly generated numbers. (a) Note that two dice are distinct. The answer is 6 × 6 = 36. (b) For the sum to be a > 6, note that either number is at most 6. The possibilities are (6 , a - 6) , (5 , a - 5) , · · · , ( a - 6 , 6) . There are 6 - ( a - 6) + 1 = 13 - a such possibilities. Then the answer is (13 - a ) / 36. (c) See part (b). (d) There are six possibilities: (1 , 1) , (2 , 2) , (3 , 3) , (4 , 4) , (5 , 5) , (6 , 6). The answer is 6 / 36 = 1 / 6. 2. With no restriction, there are ( 5 3 ) = 10 samples. (a) Two different problems might show up for this part: If the problem for you is “the governor is included in the sample”, the number of such samples is ( 4 2 ) = 6. Then the answer is 6 / 10 = 0 . 6. If the problem for you is “he governor and the treasurer are included in the sample”, the number of such samples is ( 3 1 ) = 3. Then the answer is 3 / 10 = 0 . 3. (b) Two different problems might show up for this part: If the problem for you is “the governor and the attorney general are included in the sample”, there are ( 3 1 ) = 3 such samples. Then the answer is 3 / 10 = 0 . 3.
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