pLease help me with 14th sum
correct options are A,C

Dear student,

Please find below the solution to the asked query:

A  PA/BPA+PB-1PB, PB0 is always true.Note that this statement is always true.By definition of conditional probability, we get,     PA/B=PABPB ,PB0  ....1Also we have,    PAB=PA+PB-PABPAB=PA+PB-PAB   .....2Note that,  PABPU=1  PAB1 -PAB-1    ....3From 2 and 3, we get    PABPA+PB-1Use this in 1 to get,  PA/BPA+PB-1PB ,PB0B  PAB=PA-PABThis statement is false.C  PAB=1-PAc PBc,  if A and B are independentThis statement is always true.Note that,    PAB=PA+PB-PABSince A and B are independent, we get   PAB=PA PBThis gives,   PAB=PA+PB-PA PB                  =PA+PB1-PA                  =1-PAc+PB PAc                  =1-PAc1-PB                  =1-PAc PBcThus it is proved that,     PAB=1-PAc PBc, if A and B are independentD PAB=1-PAc PBc,  if A and B are disjointThis statement is false.Note that,    PAB=PA+PB-PABSince A and B are disjoint, we get   PAB=P=0This gives,   PAB=PA+PB-0                  =PA+PBThus the correct statament is,     PAB=PA+PB, if A and B are disjoint

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