Let and be two events such that and

MATHEMATICS · Subjective · A Level · Mathematics · Probability · Probability

Problem

Let

A

and

B

be two events such that

P(A)=0.45

and

P(A\cup B)=0.70

. It is known that

A

and

B

are independent. (a) Find

P(B)

. (b) Verify that your answer satisfies the information given in the question. (c) Let

\overline B

denote the complement of

B

. Prove that if

A

and

B

are independent, then

A

and

\overline B

are also independent. (d) Using the result in part (c), find

P(A\cap \overline B)

and confirm that it equals

P(A)P(\overline B)