ag wrote:

if someone wants to estimate the probability of player #2 the long way:

probability that player #1 draws a white rock is 5/6, black rock is 1/6

if player 1 draws a white rock, player 2 then has a 1/5 probability of drawing a black rock, probability of both these events is (5/6*1/5) = 1/6

if player 1 draws a black rock, player 2 then has a 0/5 probability of drawing a black rock, probability of both these events is (1/6*0/5) = 0

adding both possibilities = 1/6 + 0 = 1/6 probability of player #2 drawing a black rock

or the other way:

if player 1 draws a white rock, player 2 then has a 4/5 probability of drawing a white rock, probability of both these events is (5/6*4/5) = 4/6

if player 1 draws a black rock, player 2 then has a 5/5 probability of drawing a white rock, probability of both these events is (1/6*5/5) = 1/6

adding both possibilities = 4/6 + 1/6 = 5/6 probability of player #2 drawing a white rock

This is correct.