1. The problem statement, all variables and given/known data Roll a 6-sided die 5 times. Event X is when a 1,2,3 shows up. Event Y is when 4,5 show up. Show the joint PMF. 2. Relevant equations 3. The attempt at a solution So... here is where im at... X~Bin(5,0.5) & Y~Bin(5,1/3) P(X=x)=(5 C x)(.5^5) & P(Y=y)=(5 C y)(1/3)^y (2/3)^(5-y) Also the events are dependent... which is where my confusion comes from Originaly I did not realize it was dependant and I found all the joint probabilities by doing p(x,y)=p(x)p(y), but this is not correct because you cannot have X=4 & Y=3 Then I tried conditional probabilitys... P(X=x,Y=y) = P(x)*P(y|x)=(5 C x)(.5^5)*((5-x) C y)(1/3)^y (2/3)^(5-y) but this is not working out either. What am I doing wrong. Am I missing something?