So, I got this from my textbook and it makes sense:

\(P_{Y|x}(y)= P(Y=y|X=x) = P_{X,Y}(x, y)/P_X(x)\)

But I'm trying to apply it to this question and I'm struggling. Here's the question:

Suppose a die is rolled six times. Let X be the total number of 4’s that occur and let Y be the number of 4’s in the first two tosses. Find \(P_{Y|x}(y)\).

What I've got so far:

\(P_X(x) = ((1/6)^x)((5/6)^{6-x})(_6C_x)\)

but now I need to find \(P_{X,Y}(x,y)\) and I'm kind of lost. What do I do next?

\(P_{Y|x}(y)= P(Y=y|X=x) = P_{X,Y}(x, y)/P_X(x)\)

But I'm trying to apply it to this question and I'm struggling. Here's the question:

Suppose a die is rolled six times. Let X be the total number of 4’s that occur and let Y be the number of 4’s in the first two tosses. Find \(P_{Y|x}(y)\).

What I've got so far:

\(P_X(x) = ((1/6)^x)((5/6)^{6-x})(_6C_x)\)

but now I need to find \(P_{X,Y}(x,y)\) and I'm kind of lost. What do I do next?

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