Let
A
= {A child has received the tetanus vaccination},
 =
{A child has
received a flu shot}, and
C
= {A child has received the mumps vaccination}. Assume
thatPr[^]+Pr[B]+Pr[C] = 1.8.
(a) If
Pr
\A U B] =
0.70, then does Boole's inequality help us determine the range
of possible values for Pr[C]? Explain your answer.
(b) If
Pr
[A
U JB] = 0.85, then what is the range of possible values for Pr[C]?
(c) Suppose that all children who receive a mumps vaccination also receive a
tetanus vaccination and that no child who receives the flu shot receives the
mumps vaccination. Also assume that Pr[AUB] = 0.85 and Pr[C] = 0.2. What
is the probability that a child receives at least one of the three vaccinations?
(Hint:
VT[AU
Â
UC]
= Pr[A}+
Pr[5]+ P r [ C ] - P r [ A B ] -PT[AC]-PT[BC] +
Vr
[ABC}.)