A letter is chosen at random from the English alphabet.

MATHEMATICS · Multi-part · CBSE · Mathematics · Probability · Probability

Problem

A letter is chosen at random from the English alphabet. (i) Construct two non-empty events

C

and

D

that are complementary. List each event as a subset of the sample space and explain why they are complementary. (ii) Construct two non-empty events

E

and

F

that are mutually exclusive but not exhaustive. Write the sets explicitly and justify both properties. (iii) Construct three events

G, H

and

K

that are exhaustive and pairwise mutually exclusive. List the subsets chosen and explain your reasoning.