1. Given that events A and B are dependent, P(A)=20%, P(BIA)=25%. What is P(A and B)?
P(BIA)=[P(A and B)]/P(A)
it follows then that:
P(A and B)=P(A)*P(BIA)
P(A)=0.2
P(BIA)=0.25
hence
P(A and B)=0.2*0.25=0.05=5%
2. Given that P(A) =12%, P(B)=48% and P(A or B)=50%. What is P(A and B)?
P(A or B)=P(A)+P(B)-P(A and B)
but
P(A)=12%, P(B)=48%, P(A and B)=50%
thus
P(A or B)=12%+48%-50%
simplifying the above we obtain:
P(A or B)=60%-50%=10%