Probabilities involving two dice

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 events:

Event A

: The sum is greater than 9

.

Event B

: The sum is an odd number.

Write your answers as exact fractions. 

Answer 1

The easiest way to do this is to make a table representing the sample space.

Write 1 to 6 across the top of the table and 1 to 6 down the left side.

At the intersection of each row and column write the sum of the number and the top and the one at the left.

You will have 36 outcomes...the denominator in your probability problem.

Now count up the intersection points which satisfy the questions. Divide this number by 36 and you have your probability.

P.S.

There is a way to represent the distribution function of the random variable which is the sum of two random variables, but it is neither necessary nor useful for this problem.