We have 12 balls four of which are white and 8 black Three p

We have 12 balls, four of which are white and 8 black. Three players A,B, then C each draw a ball in turn, the winner is the one who firsts draws a white ball. Assuming that each black ball is replaced after being drawn, find the ratio of the chances of the three players.

Solution

For the first round, A has a P of 1/3,

B has a P of (2/3)1/3,

while C has a P of (2/3)21/3.

For each subsequent round, the ratio of their chances are the same.

Thus their probabilities remain in the ratio 9:6:4.

So P(A)=9/19,

P(B)=6/19,

P(C)=4/19.