10. Show that P

n i=1 Ei



n i=1 P(Ei)

This is known as Boole’s inequality.

Hint:

Either use Equation (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.