Consider the following dice game, as played at a certain gambling casino: Players 1 and 2...

Consider the following dice game, as played at a certain gambling casino: Players 1 and 2 roll a pair of dice in turn. The bank then rolls the dice to determine the outcome according to the following rule: Player i, i = 1, 2, wins if his roll is strictly greater than the bank’s. For i = 1,2, let

and show that I1 and I2 are positively correlated. Explain why this result was to be expected.