A jug contains 5 black marbles and 5 white marbles well mixed. A marble is removed and its color noted. A second marble is removed, without replacing the first marble, and its color is also noted. If x is the total number of black marbles in the two draws, then x has a binomial distribution.

While the probability of drawing a black marble increases on the second draw if the first marble drawn was black, the probability distribution is not binomial because the probability of success (drawing a black marble) is not constant across trials. Therefore, x does not have a binomial distribution.