1. Suppose that the first ball is not replaced before the second ball is drawn. Find the probability that both balls are red.
2. Was your intuitive guess in part 1 correct?
3. Do you think that the expected number of red balls drawn is higher if the balls are drawn with replacement or without replacement?
An urn contains four red balls and six white balls. Suppose that two balls are drawn at random from the urn, and let X be the number of red balls drawn. The probability of obtaining two red balls depends on whether the balls are drawn with or without replacement. The purpose of this project is to show that the expected number of red balls drawn is not affected by whether or not the first ball is replaced before the second ball is drawn. The idea for this project was taken from the article "An Unexpected Expected Value," by Stephen Schwartzman, which appeared in the February 1993 issue of The Mathematics Teacher.