First we consider the Wallenius model. The probability that the red ball is not taken in the first draw is 1000/2000 = ½. The probability that the red ball is not taken in the second draw, under the condition that it was not taken in the first draw, is 999/1999 ≈ ½. The probability that the red ball is not taken in the third draw, under the condition that it was not taken in the first two draws, is 998/1998 ≈ ½. Continuing in this way, we can calculate that the probability of not taking the red ball in "n" draws is approximately 2−n as long as "n" is small compared to "N". In other words, the probability of not taking a very heavy ball in "n" draws falls almost exponentially with "n" in Wallenius’ model. The exponential function arises because the probabilities for each draw are all multiplied together.