Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
name: e-mail: check if faculty: class and professor: The problems of the week are available online at http://www.math.jmu.edu/∼rosenhjd/POTW.html. Solution to Problem of the Week Five A box contains 999, 999 white marbles and 1, 000, 001 black marbles. You also have an essentially endless pile of black marbles outside of the box. You reach into the box and remove two marbles at random. If they are of different colors, you place the white marble back in the box and discard the black one. If they are of the same color, you remove both of them and place one black marble from your pile into the box. Notice that each time you repeat this process, the number of marbles in the box goes down by one. Continue this process until only one marble remains in the box. What is the probability that the one remaining marble is black? The probability is zero that the one remaining marble is black. Notice that white marbles only leave the box in pairs. That means that each time you repeat the process the number of white marbles in the box either remains the same or decreases by two. Since there are an odd number of white marbles in the box to start with, it follows that the number of white marbles in the box will always be odd. Consequently, you will never be able to remove the last white marble from the box. When only one marble remains, it has to be white.