Events and are independent

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

Problem

Events

A

and

B

are independent. It is given that the probability that at least one of the events occurs is

0.56

, and the probability that

A

does not occur while

B

occurs is

0.14

. Solve the following. (i) Form two equations involving

P(A)

and

P(B)

using the given information. (ii) Solve the equations to obtain

P(A)

P(B)

, and

P(A\cap B)

. (iii) Hence find the probability that neither

A

nor

B

occurs.