[3 pts). Let A1,. , An be independent events. Show that
P(A1U... U An) = 1- II (1 - P(Ax)) > 1 – exp (ΣΑ) P(Ak) k=1 V
(Hint: e-*>1- x for all x E R.)
[3 pts] You and one of your study group members toss a fair coin n times. Show that the probability that both of you toss the same number of heads is (2n n)2^-2n. (Note: There are several ways to derive this probability; in particular, there is one way which does not require any calculation at all!)
