Let A and B be two events in a sample space S such that
P(A)=.6 P(B)=.5 and P(A intersect B) =.2 Find
A) P(A|B)
B) P(B|A)
Please explain how to do this! Thank you
A) P(A intersect B) = P(A|B)*P(B) Replacing the known vallues: 0.2=P(A|B)*0.5 Solving for P(A|B): 0.2/0.5=P(A|B)*0.5/0.5 0.4=P(A|B) P(A|B)=0.4
B) P(B intersect A) = P(B|A)*P(A) Replacing the known vallues: 0.2=P(B|A)*0.6 Solving for P(B|A): 0.2/0.6=P(B|A)*0.6/0.6 2/6=P(B|A) 1/3=P(B|A) P(B|A)=1/3
