Ten identically shaped discs are in a bag; two of them are black, the rest white. Discs are drawn at random from the bag in turn and not replaced. Let X be the number of discs drawn up to and including the first black one. List the values of X and the associated theoretical probabilities. Calculate the mean value of X and its standard deviation. What is the most likely value of X? If, instead, each disc is replaced before the next is drawn, construct a similar list of values and point out the chief differences between the two lists.