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
The Correct answer is C.
Explanation
The outcome space for this experiment is the set of all ordered pairs 
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:
Among all the pairs 
, 
are pairs for which 
. So 
remaining pairs will have 
. Notice that the number of pairs 
for which 
is the same with the number of pairs
for which 
. Therefore the number of pairs
for which 
, is 
(half of 
). Then the probability that 
is equal to 
.
