Let A1 and A2 form a partition of sample space S, with

P(A1)=.4 and P(A2)=.6

Assume E is an event in S with P(E l A1)=.05 and P(E l A2)=.08

what would P(E) equal?
and what would P(A1 l E) equal?

2. Originally Posted by letsbeclichex
Let A1 and A2 form a partition of sample space S, with

P(A1)=.4 and P(A2)=.6

Assume E is an event in S with P(E l A1)=.05 and P(E l A2)=.08

what would P(E) equal?
and what would P(A1 l E) equal?
P(E)=P(E|A1)P(A1)+P(E|A2)P(A2)

P(A1|E)=P(E|A1)P(A1) / [P(E|A1)P(A1) + P(E|A2)P(A2)]