I'd like your help with the following exercise I found in a set of difficult -at least for me- exercises. There is a box that contains 10 White, 20 Black and 30 Red balls, we choose 4 with replacement.
a. What's the probability we chose at least one White ball?
b. What's the probability we chose at least one White ball taking into account we didn't choose any Red ones?(conditional)
c. What's the probability we didn't choose any Red balls, taking into account that we chose at least one White ball?(conditional)
So, b. and c. have to do with a. For a. I thought I could find the probability that I didn't choose any white balls.
The possible outcomes are: $\binom{20}4+\binom{20}3\binom{30}1+\binom{20}2\binom{30}2+\binom{20}1\binom{30}3+\binom{30}4$
Our sample space is: $\binom{60}4$
I don't know if I'm thinking of it correctly but that's what I've came up with so far.