Conditional Probability for discrete random variables.

[XodoX]

Homework Statement

Compute P(X=k l X+Y=p)

Homework Equations

The Attempt at a Solution

No idea. Kind of understand page #1. Although it seems like there's a lot of unnecessary stuff. Could have gone straight from the top to the bottom. And I don't know why/if you even have to substitute the X+Y=p for Y=k-p. Totally lost on page 2. No idea what's going on there. Says it's being split up because it's independent, but no idea where the 1/3 and 2/3 for 0 and 1 come form. Let alone the rest of page 2.
So, in short: What's exactly step 1,2,3 etc. ?

 

[Ray Vickson]

Homework Statement

Compute P(X=k l X+Y=p)

Homework Equations

The Attempt at a Solution

No idea. Kind of understand page #1. Although it seems like there's a lot of unnecessary stuff. Could have gone straight from the top to the bottom. And I don't know why/if you even have to substitute the X+Y=p for Y=k-p. Totally lost on page 2. No idea what's going on there. Says it's being split up because it's independent, but no idea where the 1/3 and 2/3 for 0 and 1 come form. Let alone the rest of page 2.
So, in short: What's exactly step 1,2,3 etc. ?

The 1/3 and 2/3 for 0 and 1, etc., are just examples, so the writer has some definite numbers to work with when practicing use of the formulas.

RGV

 

[mathmajor23]

I'm also trying to solve this similar problem, and also have no idea how to go about solving it.

 

[Ray Vickson]

I'm also trying to solve this similar problem, and also have no idea how to go about solving it.

For two events A and B we have
$$P(A|B) = \frac{P(A \cap B)}{P(B)}.$$

That's all there is to it. Just figure out what are the events A and B in your problem.

RGV