Mathematics

Problem

Consider an event

E

in a finite sample space

S

. Answer the following: a. (i) Define the complement

E'

of an event

E

. b. (ii) Prove that

P(E) + P(E') = 1

for any event

E

S

. c. (iii) Explain, in your own words, why the range

0 \le P(E) \le 1

follows directly from the result in part (ii).