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主题：[The Official SAT Question of the Day™] January 12th Monday

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A 6-sided number cube, with faces numbered 1 through 6, is to be rolled twice. What is the probability that the number that comes up on the first roll will be less than the number that comes up on the second roll?
A.

B.

C.

D.

E.

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SAT题目：http://apps.collegeboard.com/qotd/question.do

楼主 Date: 2009-01-12 13:26:03

jasontomonaga

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Hint : For the two numbers that will come up there are three possibilities: 1)the first number is less than the second 2)they are equal 3)the first number is greater than the second

沙发 Date: 2009-01-12 13:27:13

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Correct Answer: C

Here's Why: The outcome space for this experiment is the set of all ordered pairs (a,b) where a represents the first number that comes up, and b represents the second one. Since a and b can take all the values 1 through 6, there will be a total of 36 possible outcomes. The outcomes can be represented in a table as shown:

Among all the pairs (a,b), 6 are pairs for which a = b. So 30 remaining pairs will have a ≠ b. Notice that the number of pairs (a,b) for which a < b is the same with the number of pairs (a,b) for which a > b . Therefore the number of pairs (a,b) for which a < b, is 15 (half of 30). Then the probability that a < b is equal to .
Question Type: Standard Multiple Choice
(Mathematics)

板凳 Date: 2009-01-12 13:27:52