6. An urn contains four red and four black balls. A sample of two balls is drawn at random. If both balls drawn are of the same color, these balls are set aside and a new sample is drawn. If the two balls drawn are of different colors, they are returned to the urn and another sample is drawn. Assume that the draws are independent and that the same sampling plan is pursued at each stage until all balls are drawn.

(a) Find the probability that at least n samples are drawn before two balls of the same color appear.

(b) Find the probability that after the first two samples are drawn four balls are left, two black and two red.