Prove the Inclusion-Exclusion formula (see Theorem 1.3.7) for n = 4 under the assumption that the sample space is finite or countably infinite. (Hint: Let x be an arbitrary simple event. Suppose that...

Prove the Inclusion-Exclusion formula (see Theorem 1.3.7) for n = 4 under the assumption

that the sample space is finite or countably infinite. (Hint: Let x be an arbitrary simple

event. Suppose that x is contained in exactly k of the sets A1,A2,A3,A4, where k = 1,2,3,

or 4. Show that the probability of x is counted exactly once on the right-hand side of (1.14).