42. Consider the following dice game, as played at a certain gambling casino:

Players 1 and 2 roll in turn a a pair of dice. The bank then rolls the dice determine the outcome according to the following: player i, 1, 2, wins if his roll is strictly greater than the bank's. Let for i = 1, 2, I =

{

if i wins 0 otherwise and show that I, and I₂ are positively correlated. Explain why this result was to be expected.