SAT官方每日一题1月16日：Mathematics

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2012-01-16 13:01

Read the following SAT test question and then click on a button to select your answer.

A 6-sided number cube, with faces numbered through , 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?

The correct answer is C

Explanation

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

math graphic

Among all the pairs (a comma b) , are pairs for which a = b . So remaining pairs will have a not equal to b . Notice that the number of pairs for which a less than b is the same with the number of pairs

(a comma b) for which a greater than b . Therefore the number of pairs

(a comma b) for which a less than b , is (half of ). Then the probability that is equal to (number of pairs (a comma b) comma where a less than b) over (number of all possbile outcomes = 15 over 36 = 5 over 12 .

(责任编辑：淡笑)

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