Show that P

n i=1 Ei



n i=1 P(Ei )

This is known as Boole’s inequality.

H int: Either use Eq. (1.2) and mathematical induction, or else show that n i=1 Ei = n i=1 Fi , where F1 = E1,Fi = Ei i−1 j=1 Ec j , and use property (iii)

of a probability.