Two events and of a sample space satisfy and .

MATHEMATICS · Multi-part · A Level · Mathematics · Probability · Probability

Problem

Two events

C

and

D

of a sample space satisfy

C\cup D = S

and

C\cap D \neq \emptyset

. (i) Are

C

and

D

mutually exclusive? Give Yes or No with a one-sentence reason. (ii) Are

C

and

D

exhaustive? Give Yes or No with a one-sentence reason.