Probability, without replacement An urn contains 11 balls, of which 4 are white. Three players $A$, $B$, and $C$, successively draw from the urn. $A$ first, then $B$, then $C$, then $A$ again, and so on. The winner is the first one to draw a white ball. Find the probability of winning for each player, assuming the balls that are withdrawn are not replaced.  
Find $\mathbf{P}(A \text{ wins})$
Find $\mathbf{P}(B \text{ wins})$
Find $\mathbf{P}(C \text{ wins})$
I have completed the same problem with replacement of the marbles. I do not know how to start without replacement. 

Assume $4$ white and $7$ red balls in the box. Then:
$$P(A)=P(W_A)+P(R_AR_BR_CW_A)+P(R_AR_BR_CR_AR_BR_CW_A)=\frac{4}{11}+\frac{7\cdot 6\cdot 5\cdot 4}{11\cdot 10\cdot 9\cdot 8}+\frac{7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 4}{11\cdot 10\cdot 9\cdot 8\cdot 7\cdot 6\cdot 5}\approx 0.4818.$$
Similarly for $P(B), P(C)$.
