Three balls are randomly drawn from an urn that contains four white and eight red balls. What is the probability of drawing a red ball on the third draw given that at least one red ball was drawn on the first two draws?

Show that the probability of drawing a club at random from a standard deck of 52 playing cards is the same as the probability of drawing the ace of hearts at random from a set of four cards consisting of the aces of hearts, diamonds, clubs, and spades.

Three people are chosen at random from a group of live men and ten women. What is the probability that all three are men?