A bag contains 4 Red and 3 Green balls. Helen and Tony play a game where, starting with Helen, they alternately draw a ball at random and do not replace it. The game finishes when a Red ball is drawn.
It is decided that each player will receive, from the other, n units if they draw the Red ball on the nth draw. Construct a table for the random variable X representing Helens winnings: thus X = 1 if Helen draws a Red on the fi rst draw, -2 if Tony draws it on the next, etc.
Calculate E(X). How much, approximately, would Helen win in a series of 100 games?