math question please help

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 8

.

Event B

: The sum is an odd number.

Write your answers as fractions.

Answer 1

You can count these out.

A) Chances 2 through 12 on A are (1,2,3,4,5,6,5,4,3,2,1) out of 36 for each sum (max at 7)

the corresponding chances of B losing given the A rolls are (0,1,3,6,10,15,21,26,30,33,35) out of 36

Mutliply these terms and sum: (1*0 + 2*1 + 3*3 + 4*6 + ...)/(36²)

B) Again, enumerating (no doubles - all even sum):

The following pairs work for B sum is odd (need odd and even)

(1,2), (1,4),(1,6),(2,3),(2,5),(3,4),(3,6),(4,5),(5,6) These can occur two ways, so 18/36

Please consider a tutor. Take care.