A bag contains $30$ buttons that are colored either blue, red or yellow. There are the same number of each color ($10$ each). A total $4$ buttons are drawn from the bag. Compute the followings:
- Find $n(\Omega)$.
- The probability that at least $3$ of them are red?
- The probability that there is at least one of each color?
This seems like a basic problem but my professor and I cannot agree on an answer.
I think the probabilities are $2/21$ and $100/203$ for parts $2$ and $3$ respectively. I used combinations to calculate the probabilities.
My professor said $n(A)/n(\Omega)$ is $3/15$ for both so that is the answer for both $2$ and $3$.