Mathematics

Problem

Let

A

and

B

be independent events on a sample space

S

. Respond to the tasks below. a. (i) Prove that the events

\overline{A}

and

\overline{B}

are also independent. b. (ii) Using part (i), derive an expression for

P(A\cup B)

in terms of

P(A)

and

P(B)

. c. (iii) Using the result from part (ii), evaluate

P(A\cup B)

and

P(\overline{A}\cap\overline{B})

when

P(A)=0.4

and

P(B)=0.5