My question is this; what is the probability of withdrawing at least one red ball and at least one blue ball from a bag with a certain number of attempts?
The requirements are, this bag has n number of balls, consisting of x-red balls, y-blue balls and z-green balls. The balls are placed back into the bag after being removed so the probability of any colour being withdrawn is constant.
In order to achieve a win at least one blue and at least one red ball must be withdrawn, e.g. if you only decide to make 3 withdrawals, then a win is one red ball, one blue ball and one ball of any colour.
My main question is, is there a formula that can be constructed to answer this question? If so what is that formula?