Math word 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 events:
Event
A
: The sum is greater than
7
.
Event
B
: The sum is an odd number.
Write your answers as exact fractions.

Answer 1

Have you been introduced to the idea of a 6-by-6 array with top row labeled 1 through 6 for possible outcomes of Die#1 and left side column labeled similarly for possible outcomes of Die#2?  Within the body, the possible totals are shown, ranging from 2 through 12.  It will be seen that total 2 occurs once only, total 3 occurs twice, total 4 occurs thrice, etc.

Total 7 occurs six times; totals 8 through 12 occur 5, , 3, 2 and 1 time, respectively.

 

This gives probabilities such as P(total 2) = 1/36, P(total 3) = 2/36, reduced to 1/18, and so forth. The most likely total is 7; its probability is 1/6.

 

THIS TABLE IS THE BASIS FOR WORKING OUT ANSWERS TO EACH AND EVERY QUESTION THAT YOU HAVE.

SOMETIMES YOU WILL HAVE TO ADD MULTIPLE INDIVIDUAL PROBABILITIES.