Question

Given the following information about events A, B, and C, determine which pairs of events, if any, are independent and which pairs and mutually exclusive. P(A)=0.02 P(A|B)=0 P(B)=0.02 P(C|B)=0.15 P(C)=0.15 P(A|C)=0.02

Answer 1

given PLA) =0.02 PCB) = 0.02 P CcJ=0.15 defination: 7 Independence: Two events A and B are said to be independent if Plan B) =PCA)XP(B) Mutual exclusive: Two events A and A and B are said to exclusive if be mutually Plano) = 8 =0 V 0.02 Now PLAIB) =0 = PLANB] P.CO PCANB=0 si PCB) = =) A and B are mutually exclusive PC CIB)= 0.15 PCCnB) = 0.15 PCB) P ( CnB)=0-15 X0-02 PCCnB) P (C) X PCB) Hence B and a are independent =

PCAIC] =0 -0.02 P.canc) 0.02 PCC) PCane) 0.02 x PCC) Planc) = Hence A and c are independent events. PCA) X PCC)