(1)
From the venn diagram in Fig 13 3, it is clear
that E ∩ F and E ∩ F′ are mutually exclusive events
and also  E =(E ∩ F) ∪ (E ∩ F′) Therefore
P(E) = P(E ∩ F) + P(E ∩ F′)
or
P(E ∩ F′) = P(E) − P(E ∩ F)
= P(E) − P(E) P(F)
(by  (1))
= P(E) (1−P(F))
= P(E)