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Mathematics>Standard Multiple Choice

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

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) 1/4
(B) 1/3
(C) 5/12
(D) 7/12
(E) 1/2

答案和解析

答案：C

解析：

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 greater than b. Therefore the number of pairs

(a , b) for which a less than b, is 15(half of 30). Then the probability that a less than b is equal to (number of pairs (a , b) comma where a less than b) over (number of all possible outcomes) = 15 over 36 = 5 over 12.