For two events and in a sample space it is given that

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

Problem

For two events

A

and

B

in a sample space it is given that

P(A)=0.60

P(A\mid B)=0.75

and

P(B\mid A)=0.50

. (i) Express

P(A\cap B)

in two different ways using the given conditional probabilities and hence obtain a single numerical value for

P(A\cap B)

. (ii) Using your answer from part (i), determine

P(B)

. (iii) Verify that all probabilities obtained satisfy

0\le P \le 1