Porisma

A hint to get started

Bound the part of C lying in B but outside A

P(A)=3/5P(A)=3/5, P(B)=3/4P(B)=3/4 and P(A∣B′)=1/2P(A\mid B')=1/2.

(i) Find P(A∩B)P(A\cap B). marks

(ii) Find P(A′∣A∪B)P(A'\mid A\cup B). marks

A third event C has P(C)=1/2P(C)=1/2 and is independent of A.

(iii) Find P(A′∩C)P(A'\cap C). mark

(iv) Hence show that 3/40≤P(A′∩B∩C)≤1/53/40\le P(A'\cap B\cap C)\le1/5. marks

[2014/AJC/II/7]

CJC · Review problems · Question 4

There is only 1/8 probability mass available outside both A and B.

Read the worked solution