Question 430376
A) A and B are not independent: P(A)*P(B)= 0.25*0.30 = 0.075.  This is not equal to P(A and B) = P(B|A)*P(A) = 0.48*0.25 = 0.12.

B) P(A and B) = P(B|A)*P(A) = 0.48*0.25 = 0.12.
C) P(A or B) = P(A) + P(B) - P(A and B) = 0.25 + 0.30 - 0.12 = 0.43
D) P(A|B) = P(A and B)/P(B) = 0.12/0.30 = 0.40
E) B and C are mutually exclusive, because it is given that P(B and C)=0 (Definition of mutual exclusivity.)

F) P(B)*P(C) = 0.30*0.55 = 0.165
P(B and C) = 0
==> The two quantities are not equal, hence B and C are not independent.