Find the Probability of Joint PDF X and Y with Easy Calculation

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Given this joint PDF of X and Y:
Code:
X\Y	1	2
0 	0.1	0.3
1	0.05	0.1
2	0.2	0.25

So:
P(X = 1| X+Y=2) = 1/2?
P(X <= 1 and Y <= 2) = 1/3?
 
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sjaguar13 said:
Given this joint PDF of X and Y:
Code:
X\Y	1	2
0 	0.1	0.3
1	0.05	0.1
2	0.2	0.25

So:
P(X = 1| X+Y=2) = 1/2?
P(X <= 1 and Y <= 2) = 1/3?

I don't get either of those. How did you get those answers?
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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