Answer the following questions on complementary events.

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

Problem

Answer the following questions on complementary events. (a) Define the complement of an event

E

in the context of a random experiment. (b) Explain why the probability of any event

E

always satisfies

0 \le P(E) \le 1

. (c) Write the algebraic relationship between

P(E)

and the probability of its complement

P(E')

. (d) If an event

F

is certain to occur, what is the value of

P(F')

? Give reason for your answer.