1) Two dice are thrown n times in succession. Compute the probability that "double 6" appears at least once. How large n need to be to make this probability 1/2?
2) An urn contains 4 red and 5 white balls. 3 balls are randomly chosen, without replacement. Finds the probability that at least one ball of each color has been chosen. Assume that the urn contains 4 red, 5 white and 6 black balls and 4 balls are randomly chosen, without replacement. Compute again the probability that at least one ball of each color has been chosen.