The Official SAT Question of the Day

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

I worked it like this for the second roll to be less than the first roll there are 0+1+2+3+4+5 = 15
And there are 6x6 probabilities in all.
So 15/36=5/12

Boffins say correct answer is C

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)