Let `E^c` denote the complement of an event `E.` Let `E,F,G` be pairwise independent events with `P(G) gt 0` and `P(E nn F nn G)=0` Then

Options

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

Answer

C

Explanation

`P((E^(c) cap F^(c))/(G))=(P(E^(c)cap F^(c)capG))/(P(G))=(P(G)-P(EcapG)-P(GcapF))/(P(G))=(P(G)[1-P(E)-P(F)])/(P(G))" "[ :' P(G) ne 0]`
`=1-P(E)-P(F)=P(E^(c)-P(F)`