Politics. In a given county, records show that of the registered voters, 45 % are Democrats, 35 % are Republicans, and 20 % are independents. In an election, 70 % of the Democrats, 40 % of the Republicans, and 80 % of the independents voted in favor of a parks and recreation bond proposal. If a registered voter chosen at random is found to have voted in favor of the bond, what is the probability that the voter is a Republican? An independent? A Democrat?
Politics. In a given county, records show that of the registered voters, 45 % are Democrats, 35 % are Republicans, and 20 % are independents. In an election, 70 % of the Democrats, 40 % of the Republicans, and 80 % of the independents voted in favor of a parks and recreation bond proposal. If a registered voter chosen at random is found to have voted in favor of the bond, what is the probability that the voter is a Republican? An independent? A Democrat?
Solution Summary: The author calculates the probability that the voter is a Republican if he has voted in favor of the parks and recreation bond proposal.
Politics. In a given county, records show that of the registered voters,
45
%
are Democrats,
35
%
are Republicans, and
20
%
are independents. In an election,
70
%
of the Democrats,
40
%
of the Republicans, and
80
%
of the independents voted in favor of a parks and recreation bond proposal. If a registered voter chosen at random is found to have voted in favor of the bond, what is the probability that the voter is a Republican? An independent? A Democrat?
Q2: Using the Laplace transform, find the solution for the following equation
y"" +y" = 6et + 6t + 6. Suppose zero initial conditions (y"" (0) = y"(0) = y'(0) = y(0) = 0).
1- Let A = {A1, A2, ...), in which A, A, = 0, when i j.
a) Is A a π-system? If not, which element(s) should be added to A to become a π-system?
b) Prove that σ(A) consists of the finite or countable unions of elements of A; i.c., A E σ(A) if and
only if there exists finite or countable sequence {n} such that A = U₁An (Hint: Let F be such
class; prove that F is a σ-filed containing A.)
c) Let p ≥ 0 be a sequence of non-negative real numbers with Σip₁ = 1. Using p₁'s, how do you
construct a probability measure on σ(A)? (Hint: use extension theorem.)
2- Construct an example for which P(lim sup A,) = 1 and P(lim inf An) = 0.
3. Let
f(z) =
sin (22) + cos (T2)
2(22+1)(z+1)
Compute f(z)dz over each of the contours/closed curves C1, C2, C3 and C4 shown
below.
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Chapter 8 Solutions
Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences (13th Edition)
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