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.
Best Answer
You are choosing with replacement, so you should just think in terms of drawing with $\frac 16$ chance of getting white, $\frac 13$ black, $\frac 12$ red. The combinations assume you are drawing without replacement. You have $\frac 56$ chance not to get white on each draw, so the chance you don't get a white one is ???