Computing a math problem

Question

An ordinary (fair) die is a cube with the numbers 1

 through 6

 on the sides (represented by painted spots). Imagine that such a die is rolled twice in succession and that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment.

compute the probability of each of the following:

event a: the sum is greater than 5

event b: the sum is divisible by 5

write your answers as exact fractions

Answer 1

The easiest way to do this problem is to write out the sample space in a 6 by 6 matrix (table).

At the intersection of each row and column put the sum of the row number and the column number.

There are 36 possibilities. Now just count the number of boxes which satisfy the conditions of the question. The probability is the number of boxes divided by 36.