stats
posted by Anonymous on .
you are given the probabilities listed below P(A)= 0.25, P(B) = 0.30, P(C)=0.55, P(A&C) = 0.05, P(B&C)=0, P(B/A)=0.48.
A) ARE A AND B INDEPENDENT?
B) FIND P(A&B)
C) FIND P(A OR B)
D) FIND P(A/B)
E) ARE B AND C MUTUALLY EXCLUSIVE EVENTS?
F) ARE B AND C INDEPENDENT EVENTS?

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(BA)*P(A) = 0.48*0.25 = 0.12.
B) P(A and B) = P(BA)*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(AB) = 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.