are there any shortcuts in answering probability questions?

Answer 1

This is my way of doing it:

Suppose you want to find the odds of rolling two sixes. The calculation is: 1/6 * 1/6 = 0.027777777777777777777777777777778 or 1 in 36.

The odds of getting one 6 is 1 in 6 or 1/6. You use multiplication because if the first one is 6 and the second is not it is absolutely useless to you. Therefore 1/6 * 1/6 = 0.027777777777777777777777777777778 or 1 in 36.

If your looking for a shortcut for something in particular post it and I will tell you what to do =)

Answer 2

YES, depending on the question I can tell you of an appropriate short cut.