Probability question

Question

1. Let P(A)=p, P(A|B)=q, P(B|A)=r. Find the relations between the number p, q, r for the following cases                                                                                                                           

a.  Events A and B are mutually exclusive

b.  Events A' and B' are mutually exclusive

c. A is a sub event of A, B is a sub event of A

Answer 1

Hi, Sakina:

For a). The answer is shown below.

P(A|B)=q => P(AB)=qP(B)

P(B|A)=r => P(AB)=rp

This means qP(B) = rp. So P(B)=rp/q.

If A and B are mutually independent, P(AB)=P(A)P(B)

So rp=p * rp/q, which means p/q =1 or p=q.