Roll a fair die twice. Let A be the event that the first roll comes up odd, B the event that the second roll is odd, and C the event that the sum of the dice is odd. Show that any two of the events A,...

Roll a fair die twice. Let A be the event that the first roll comes up odd, B the event that the second roll is odd, and C the event that the sum of the dice is odd. Show that any two of the events A, B, and C are independent but the events A, B, and C are not independent.