MATH STINGER #74
by Dr. Joel C. Fowler
Assistant Professor of Mathematics
The puzzle for this issue involves probability. A large urn contains an unknown mixture of blue and red balls. 500 balls are drawn one after another (without replacing them in the urn as they are drawn). All 500 are found to be blue. Someone who knew the original contents of the urn remarks that the probability of that outcome (i.e. all 500 blue) was exactly 1/2. Assuming that the remark was correct, find the smallest possible number of balls originally in the urn and the distribution of red and blue balls. Although a course such as Math 260 is useful in finding a solution, it is not essential. Somewhat more difficult, however, is to show that the answer has the smallest possible number of balls. For this second part of the puzzle you should have some knowledge of probability.