Each of two boxes contains marbles, and each marble is either black or white. The total number of black marbles is different from the total number of white marbles. One marble is drawn at random from each box. The probability that both marbles are white is . What is the probability that both are black?
Source: NCTM Mathematics Teacher, November 2006
Let represent the probability of drawing marbles from the first box and from the second box. Drawing a marble from one box is an independent event from drawing a marble from another box. Let represent the number of white marbles in the first box and the number of white marbles in the second box.
The possible factors that make are
The first three are not possible because are all greater than marbles.
is not possible because that would make the number of white marbles equal to the number of black marbles
white white black black.
The only solution is and or vice-versa or .