A fair six-sided die is thrown once

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

Problem

A fair six-sided die is thrown once. Let the sample space be denoted by

S

and consider the event

A

: “the number obtained is even.” Answer the following questions: (i) List explicitly all the elements of

S

. (ii) Write the set

A

and its complement

A'

. (iii) By counting outcomes, show that

P(A') = 1 - P(A)

. (iv) State, with reasons, whether

A

and

A'

are mutually exclusive events and whether they are exhaustive events.