Question

An urn initially contains 5 white and 7 black balls. Each time a ball is selected, its color is noted and
it is replaced in the urn along with two other balls of the same color. Compute the probability that
(a) one black and one white is selected.
(b) exactly two black balls are selected.

Answer 1

a)black ball=1 and white ball=1 
probability=1+1\5+7=2\12=1\6
b)2\12=1\6

Answer 2

An urn initially contains 5 white and 7 black balls. Each time a ball is selected, its color is noted and it is replaced in the urn along with 2 other balls of the same color. Compute the probability that (a) the first 2 balls selected are black and the next 2 are white; (b) of the first 4 balls selected, exactly 2 are black.