Question

(4) (a) Suppose that P(A) = P(B) = ? and that P(A|B) = P(B). Calculate P( AB') (b) Suppose that P(ANB) = , P(A|B') = and P(B) = . Calculate P(A) (c) Let A and B be events such that P(A) = if BCA and P(B']A) = Calculate P(B)

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Answer 1

Page 1 we have, pCA)=L, PCB) ,P(AIB) P(B) 4 PCAN B)=2 consides, p (A1B) = PCAN B P(B) PIAIB) - P(B) But PCANB) PCR/B) PCB) PCB) PIANB P(B) PIANB) - (P(B)) Now, P(ANB) P (A)-PCAN B) -8g usingO P(A) -P(B)J 2 4 16 4-1 16 16 PCAD B')3 16 , P(AI B')=L, b we have P(An B) = P (B) , Find PCA) we know that, P(AIB) P(AnB P(B')

page2 PCANB') PCA) - PCANB) and But PCB')= 1-P(B) Using this formulae we can write PCA18') = PCA) PCAN B) 1 P(B) PCA)-(14) 1- (112) t2 (PCA)-) = P(A ) -- 16 4 PCA= + 16 PIA)=5 16 P(B'IA)- PCB) = ? we have, PCA) = 1 and BCA AnB = A P(AnB)- P(A) Consider, P(BtA) - 5 PCBnA) 7 P(A) P(B')-P(AnB) PCA) But PCANB) -PCA) . P(B')- P(A =5 7 PCA)

Page3 PIB)-PCA) PIA)x5 atso, P(B') 1-P(B) P(B) P(A) = PCA) x5 P(A) x 5 7 1- P(B) P(A) 5 1- P(B)- 3 3 - P (B) -5 21 2 3 -PCB) 11 21 PCB) 21 e. P(B)= 7 3