 8.1: In 112, use the tree diagram below to find the indicated probabilit...
 8.2: In 112, use the tree diagram below to find the indicated probabilit...
 8.3: In 112, use the tree diagram below to find the indicated probabilit...
 8.4: In 112, use the tree diagram below to find the indicated probabilit...
 8.5: In 112, use the tree diagram below to find the indicated probabilit...
 8.6: In 112, use the tree diagram below to find the indicated probabilit...
 8.7: In 112, use the tree diagram below to find the indicated probabilit...
 8.8: In 112, use the tree diagram below to find the indicated probabilit...
 8.9: In 112, use the tree diagram below to find the indicated probabilit...
 8.10: In 112, use the tree diagram below to find the indicated probabilit...
 8.11: In 112, use the tree diagram below to find the indicated probabilit...
 8.12: In 112, use the tree diagram below to find the indicated probabilit...
 8.13: In 1332, use the tree diagram below to find the indicated probabili...
 8.14: In 1332, use the tree diagram below to find the indicated probabili...
 8.15: In 1332, use the tree diagram below to find the indicated probabili...
 8.16: In 1332, use the tree diagram below to find the indicated probabili...
 8.17: In 1332, use the tree diagram below to find the indicated probabili...
 8.18: In 1332, use the tree diagram below to find the indicated probabili...
 8.19: In 1332, use the tree diagram below to find the indicated probabili...
 8.20: In 1332, use the tree diagram below to find the indicated probabili...
 8.21: In 1332, use the tree diagram below to find the indicated probabili...
 8.22: In 1332, use the tree diagram below to find the indicated probabili...
 8.23: In 1332, use the tree diagram below to find the indicated probabili...
 8.24: In 1332, use the tree diagram below to find the indicated probabili...
 8.25: In 1332, use the tree diagram below to find the indicated probabili...
 8.26: In 1332, use the tree diagram below to find the indicated probabili...
 8.27: In 1332, use the tree diagram below to find the indicated probabili...
 8.28: In 1332, use the tree diagram below to find the indicated probabili...
 8.29: In 1332, use the tree diagram below to find the indicated probabili...
 8.30: In 1332, use the tree diagram below to find the indicated probabili...
 8.31: In 1332, use the tree diagram below to find the indicated probabili...
 8.32: In 1332, use the tree diagram below to find the indicated probabili...
 8.33: In 3338, evaluate each expression. 0!
 8.34: In 3338, evaluate each expression. (8  3)!
 8.35: In 3338, evaluate each expression. 7! 4!
 8.36: In 3338, evaluate each expression. 10! 2!8!
 8.37: In 3338, evaluate each expression. 12! 11!
 8.38: In 3338, evaluate each expression. 6! (6  3)! 3!
 8.39: In how many different ways can a committee of 3 people be formed fr...
 8.40: In how many different ways can 4 people line up?
 8.41: In how many different ways can 3 books be placed on a shelf?
 8.42: In how many different ways can 3 people be seated in 4 chairs?
 8.43: You are to set up a code of 3digit words using the digits 1, 2, 3,...
 8.44: You are to set up a code of 2digit words using the digits 1, 2, 3,...
 8.45: Forming Committees There are 7 boys and 6 girls willing to serve on...
 8.46: Choosing DoubleDip Cones Juans Ice Cream Parlor offers 31 differen...
 8.47: Arranging Books A person has 4 history, 5 English, and 6 mathematic...
 8.48: Choosing Names A newborn child can be given 1, 2, or 3 names. In ho...
 8.49: Forming Committees In how many ways can a committee of 8 boys and 5...
 8.50: Football Teams A football squad has 7 linemen, 11 linebackers, and ...
 8.51: There are 5 rotten plums in a crate of 25 plums. How many samples o...
 8.52: An admissions test given by a university contains 10 truefalse ques...
 8.53: How many 6letter words (real or imaginary) can be made from the wo...
 8.54: How many 7letter words (real or imaginary) can be made from the wo...
 8.55: Arranging Books Jessica has 10 books to arrange on a shelf. How man...
 8.56: Arranging Pennants Mike has 9 pennants to arrange on a pole. How ma...
 8.57: Rolling a Loaded Die A die is loaded so that when it is rolled an o...
 8.58: The records of Midwestern University show that in one semester, 38%...
 8.59: In a certain population of people, 25% are blueeyed and 75% are br...
 8.60: College Majors At a local college 55% of the students are female an...
 8.61: Score Distribution Two forms of a standardized math exam were given...
 8.62: ACT Scores The following data compare ACT scores of students with t...
 8.63: E and F are independent events. Find if and
 8.64: E and F are independent events. Find P(E) if and
 8.65: Shooting Free Throws A basketball player hits 70% of his free throw...
 8.66: Majoring in Business At the College at Old Westbury, 20% of the stu...
 8.67: Three envelopes are addressed for 3 secret letters written in invis...
 8.68: Jones lives at O (see the figure). He owns 5 gas stations located 4...
 8.69: Defective Machine The calibration of a filling machine broke, causi...
 8.70: Broken Calculators Three broken calculators were inadvertently pack...
 8.71: Quality Control In a factory three machines, produce 55%, 30%, and ...
 8.72: Test for Cancer A lung cancer test has been found to have the follo...
 8.73: Advertising Management believes that 1 out of 5 people watching a t...
 8.74: Baseball Suppose that the probability of a player hitting a home ru...
 8.75: Tossing Coins What is the expected number of heads when a coin is t...
 8.76: Recovery Rate The recovery rate from a flu is 0.9. If 4 people have...
Solutions for Chapter 8: Additional Probability Topics
Full solutions for Finite Mathematics, Binder Ready Version: An Applied Approach  11th Edition
ISBN: 9780470876398
Solutions for Chapter 8: Additional Probability Topics
Get Full SolutionsChapter 8: Additional Probability Topics includes 76 full stepbystep solutions. Finite Mathematics, Binder Ready Version: An Applied Approach was written by and is associated to the ISBN: 9780470876398. This textbook survival guide was created for the textbook: Finite Mathematics, Binder Ready Version: An Applied Approach, edition: 11. Since 76 problems in chapter 8: Additional Probability Topics have been answered, more than 16764 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions.

Complete solution x = x p + Xn to Ax = b.
(Particular x p) + (x n in nullspace).

Complex conjugate
z = a  ib for any complex number z = a + ib. Then zz = Iz12.

Distributive Law
A(B + C) = AB + AC. Add then multiply, or mUltiply then add.

Full column rank r = n.
Independent columns, N(A) = {O}, no free variables.

Incidence matrix of a directed graph.
The m by n edgenode incidence matrix has a row for each edge (node i to node j), with entries 1 and 1 in columns i and j .

Kirchhoff's Laws.
Current Law: net current (in minus out) is zero at each node. Voltage Law: Potential differences (voltage drops) add to zero around any closed loop.

Left nullspace N (AT).
Nullspace of AT = "left nullspace" of A because y T A = OT.

Length II x II.
Square root of x T x (Pythagoras in n dimensions).

Norm
IIA II. The ".e 2 norm" of A is the maximum ratio II Ax II/l1x II = O"max· Then II Ax II < IIAllllxll and IIABII < IIAIIIIBII and IIA + BII < IIAII + IIBII. Frobenius norm IIAII} = L La~. The.e 1 and.e oo norms are largest column and row sums of laij I.

Orthogonal matrix Q.
Square matrix with orthonormal columns, so QT = Ql. Preserves length and angles, IIQxll = IIxll and (QX)T(Qy) = xTy. AlllAI = 1, with orthogonal eigenvectors. Examples: Rotation, reflection, permutation.

Projection matrix P onto subspace S.
Projection p = P b is the closest point to b in S, error e = b  Pb is perpendicularto S. p 2 = P = pT, eigenvalues are 1 or 0, eigenvectors are in S or S...L. If columns of A = basis for S then P = A (AT A) 1 AT.

Random matrix rand(n) or randn(n).
MATLAB creates a matrix with random entries, uniformly distributed on [0 1] for rand and standard normal distribution for randn.

Row picture of Ax = b.
Each equation gives a plane in Rn; the planes intersect at x.

Singular matrix A.
A square matrix that has no inverse: det(A) = o.

Skewsymmetric matrix K.
The transpose is K, since Kij = Kji. Eigenvalues are pure imaginary, eigenvectors are orthogonal, eKt is an orthogonal matrix.

Stiffness matrix
If x gives the movements of the nodes, K x gives the internal forces. K = ATe A where C has spring constants from Hooke's Law and Ax = stretching.

Symmetric matrix A.
The transpose is AT = A, and aU = a ji. AI is also symmetric.

Trace of A
= sum of diagonal entries = sum of eigenvalues of A. Tr AB = Tr BA.

Triangle inequality II u + v II < II u II + II v II.
For matrix norms II A + B II < II A II + II B II·

Vector space V.
Set of vectors such that all combinations cv + d w remain within V. Eight required rules are given in Section 3.1 for scalars c, d and vectors v, w.