A die is tossed twice and the number of dots facing up noted in the
order of occurrence. Assuming that all outcomes are equally likely to
occur, fin the probabilities of the following events:

a.   Ak:  the sum of the two outcomes is k, for k = 2,......,12.
b.   B:   the outcomes of the two tosses are different.

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Clarification of Question by alpa101473-ga on 07 Sep 2003 07:44 PDT

give explanation of answer. Thanx

Hello and thank you for your question.

Question A:
Take a look at the picture at the top of the following webpage - - it
shows that there are 36 possible outcomes when you roll one die twice
(which is the same as rolling a pair of dice).
Dice Probability Table
http://www.dicesetter.com/general/diceprob.htm

So as shown on that page the probabilities are
There is one way to make the two and twelve.  probability = 1/36 each
There are two ways to make the three and eleven. probability = 2/36 =
1/18 each
There are three ways to make the four and ten. probability = 3/36 =
1/12 each
There are four ways to make the five and nine. probability = 4/36 =
1/9 each
There are five ways to make the six and eight. probability = 5/36 each
There are six ways to make the seven. probability = 6/36 = 1/6 

Question B

Here we're not adding two rolls, so it's more simple.
After you've made the first roll one of the six faces is the one you
'don't' want to get, and five of the six faces are 'OK' to get.
So the outcome of the two tosses will be different 5/6ths of the time.

Search term used:
dice probability table

Thanks again for letting us help
Richard-ga