Let and be two events such that and for some real number

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

Problem

Let

A

and

B

be two events such that

P(A)=2t

and

P(B)=3t

for some real number

t>0

. The events are known to be independent and

P(A\cup B)=0.8

. (a) Establish an equation in

t

using the given information and solve for all values of

t

that lie in

(0,1)

. (b) For each permissible value of

t

obtained in part (a), compute

P(A\cap B)

. (c) Discuss whether more than one value of

t

satisfies all axioms of probability and give a brief explanation for your conclusion.