[jay_shark]

For the probability you have at least 1 red marble it is best that you take the complement for when you select no red marbles .

P(r=0) = c(x-y,z)/c(x,z)
p(r=1)+p(r=2)+...+P(r=y)= 1-P(r=0) = 1-c(x-y,z)/c(x,z)

b)Since we know p(r=0) , we need to figure out p(r=1) .
c(y,1)c(x-y,z-1)/c(x,z).
So now take 1-p(r=0)-p(r=1) to get your answer .

c) Just add p(r=0)+p(r=1) since these probabilities are independent .