A French nobleman, Chevalier de M´er´e, had asked a famous mathematician, Pascal, to explain why the following two probabilities were different (the difference had been noted from playing the game many times): 

(1) At least one six in four independent casts of a six-sided die; 

(2) At least a pair of sixes in 24 independent casts of a pair of dice. From proportions it seemed to de M´er´e that the probabilities should be the same. Compute the probabilities of (1) and (2).