SAT Question of the Day July 15th 2013

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 over 4

B.     1 over 3

C.     5 over 12

D.     7 over 12

E.     1 over 2

We have a probability question on our hands.

There are a few ways to attack this problem and get to the right answer.

The easiest way, in my opinion, to solve this question is unfortunately the most time demanding.

We have 6X6=36 possible outcomes – lets write them down:

In the table we’ll make we will place the number that can come up in the first roll and we will mark the desired outcomes of the second roll (with a value less than and not including the value we got on the first roll) in parentheses.

First roll   Second roll              number of options that satisfy the criteria

1                 1, 2, 3, 4, 5, 6                                                 0

2                 (1), 2, 3, 4, 5, 6                                               1

3                 (1, 2), 3, 4, 5, 6                                               2

4                 (1, 2, 3), 4, 5, 6                                               3

5                 (1, 2, 3, 4), 5, 6                                               4

6                 (1, 2, 3, 4, 5), 6                                               5

Summing up the desired outcomes we obtain 15 out of 36 or 5/12.

This is one of those problems that can be solved theoretically using formulas but lend themselves to be solved by “brute force” which also allows for us to check our work.

47% out of 184,000 got it right.

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