Event Differences. Recall that the difference between events A and B was defined as A\B = A ∩Bc. Using Venn diagrams demonstrate that
(a) A\(A\B) = A ∩ B and A\(B\A) = A,
(b) A\(B\C) = (A ∩C) ∪ (A ∩Bc ).
De Mere Paradoxes. In 1654 the Chevalier de Mere asked Blaise Pascal (1623–1662) the following two questions:
(a) Why would it be advantageous in a game of dice to bet on the occurrence of a 6 in 4 trials but not advantageous in a game involving two dice to bet on the occurrence of a double 6 in 24 trials?
(b) In playing a game with three dice, why is a sum of 11 more advantageous than a sum of 12 when both sums are the result of six configurations: 11: (1, 4, 6), (1, 5, 5), (2, 3, 6), (2, 4, 5), (3, 3, 5), (3, 4, 4); 12: (1, 5, 6), (2, 4, 6), (2, 5, 5), (3, 3, 6), (3, 4, 5), (4, 4, 4)? How would you respond to the Chevalier?