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

Options

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

Answer

C

Explanation

Clearly,
`P(E'cap F'//G)=(P(E' cap F' cap G)/(P(G)))`
`=(P(G)-P{(E cup F)capG})/(P(G))`
`=(P(G)-P(E cap G)-P(F cap G)+P(E cap F cap G))/(P(G))`
`=(P(G)-P(E )P(G)-P(F)P(G)+0)/(P(G))`
`=1-P(E )-P(F)=P(E')-P(F)`