Find two other relations for sn and mn in terms of cn−1, sn−1, and mn−1, and hence find cn, sn, and mn. (Oxford 1974M)

14.

(a) Let P(A) denote the probability of the occurrence of an event A. Prove carefully, for events A1, A2, . . . , An, that P





[n i=1 Ai



 =

X i

P(Ai ) −

X i

X i

+ (−1)n+1P





\

i Ai



.