Let A,B and C are pairwise independent events with `P ( C ) gt 0 and P(A cap B cap C ) =0`. Then , `P(((A^c cap B^c))/( C ))` is

Options

A. `P(A^(c ))+P(B^(c ))`
B. `P(A^(c ))-P(B^(c ))`
C. `P(A^(c ))- P(B)`
D. `P(A)-P(B^(c ))`

Answer

C

Explanation

`P(A^(c ) cap B^(c )//C)`
`=P((A cup B)^(c )RC)`
`=1-P((A cup B)//C)=1-(P((A cup B)cap C))/(P(C ))`
`=1-(P(A cap C) cup (B cap C))/(P(C ))`
`=1-({P(A cap C)+P(B cap C)-P(A cap B cap )})/(P(C ))`
`=1-{(P(A)P(C )+P(B)P(C )-0)/(P(C ))}`
`=1-{P(A)+P(B)}=1-P(A)-P(B)=P(A^(c ))-P(B)`