Question

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

Answer 1

P(A|B)P(A intersect B) = 0.2 = P( B intersect A)

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