Two integers X and Y are selected at random

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Question from Kenneth:

Two integers X and Y are selected at random from the integers
1 to 8.If the same integer may be selected twice,find the probability
that;
1)X-Y=2
2)X-Y is 5 or more
3)X is greater than Y

Hi Kenneth,

I would use a table to work on this problem. Below is my start to produce a table of possible outcomes.

	1	2	3	4	5	6	7	8
1
2
3
4
5
6
7
8

In my table the numbers at the top are the possible X-values and the numbers on the left side are the possible Y-values. When you select $x$ and $Y$ at random you are equally likely to end in any of the 64 possible cells in the table.

For problems 1) and 2) I would fill in the table with the values of $X - Y.$ Here are a few values.

	1	2
1	0	1
2	-1
3
4
5
6
7
8

Fill in the table and from the table answer parts 1) and 2).

Penny

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