 9.7.1: What term is used to express the likelihood of an event occurring? ...
 9.7.2: What is a sample space?
 9.7.3: What is an experiment?
 9.7.4: What is the difference between events and outcomes? Give an example...
 9.7.5: The union of two sets is defined as a set of elements that are pres...
 9.7.6: For the following exercises, use the spinner shown in Figure 3 to f...
 9.7.7: For the following exercises, use the spinner shown in Figure 3 to f...
 9.7.8: For the following exercises, use the spinner shown in Figure 3 to f...
 9.7.9: For the following exercises, use the spinner shown in Figure 3 to f...
 9.7.10: For the following exercises, use the spinner shown in Figure 3 to f...
 9.7.11: For the following exercises, use the spinner shown in Figure 3 to f...
 9.7.12: For the following exercises, use the spinner shown in Figure 3 to f...
 9.7.13: For the following exercises, use the spinner shown in Figure 3 to f...
 9.7.14: For the following exercises, two coins are tossed. What is the samp...
 9.7.15: For the following exercises, two coins are tossed. Find the probabi...
 9.7.16: For the following exercises, two coins are tossed. Find the probabi...
 9.7.17: For the following exercises, two coins are tossed. Find the probabi...
 9.7.18: For the following exercises, four coins are tossed. What is the sam...
 9.7.19: For the following exercises, four coins are tossed. Find the probab...
 9.7.20: For the following exercises, four coins are tossed. Find the probab...
 9.7.21: For the following exercises, four coins are tossed. Find the probab...
 9.7.22: For the following exercises, four coins are tossed. Find the probab...
 9.7.23: For the following exercises, four coins are tossed. Find the probab...
 9.7.24: For the following exercises, four coins are tossed. Find the probab...
 9.7.25: For the following exercises, four coins are tossed. Find the probab...
 9.7.26: For the following exercises, one card is drawn from a standard deck...
 9.7.27: For the following exercises, one card is drawn from a standard deck...
 9.7.28: For the following exercises, one card is drawn from a standard deck...
 9.7.29: For the following exercises, one card is drawn from a standard deck...
 9.7.30: For the following exercises, one card is drawn from a standard deck...
 9.7.31: For the following exercises, one card is drawn from a standard deck...
 9.7.32: For the following exercises, one card is drawn from a standard deck...
 9.7.33: For the following exercises, two dice are rolled, and the results a...
 9.7.34: For the following exercises, two dice are rolled, and the results a...
 9.7.35: For the following exercises, two dice are rolled, and the results a...
 9.7.36: For the following exercises, two dice are rolled, and the results a...
 9.7.37: For the following exercises, two dice are rolled, and the results a...
 9.7.38: For the following exercises, two dice are rolled, and the results a...
 9.7.39: For the following exercises, two dice are rolled, and the results a...
 9.7.40: For the following exercises, two dice are rolled, and the results a...
 9.7.41: For the following exercises, two dice are rolled, and the results a...
 9.7.42: For the following exercises, two dice are rolled, and the results a...
 9.7.43: For the following exercises, a coin is tossed, and a card is pulled...
 9.7.44: For the following exercises, a coin is tossed, and a card is pulled...
 9.7.45: For the following exercises, a coin is tossed, and a card is pulled...
 9.7.46: For the following exercises, a coin is tossed, and a card is pulled...
 9.7.47: For the following exercises, use this scenario: a bag of M&Ms conta...
 9.7.48: For the following exercises, use this scenario: a bag of M&Ms conta...
 9.7.49: For the following exercises, use this scenario: a bag of M&Ms conta...
 9.7.50: For the following exercises, use this scenario: a bag of M&Ms conta...
 9.7.51: Use the following scenario for the exercises that follow: In the ga...
 9.7.52: Use the following scenario for the exercises that follow: In the ga...
 9.7.53: Use the following scenario for the exercises that follow: In the ga...
 9.7.54: Use the following scenario for the exercises that follow: In the ga...
 9.7.55: Use the following scenario for the exercises that follow: In the ga...
 9.7.56: Use this data for the exercises that follow: In 2013, there were ro...
 9.7.57: Use this data for the exercises that follow: In 2013, there were ro...
 9.7.58: Use this data for the exercises that follow: In 2013, there were ro...
 9.7.59: Use this data for the exercises that follow: In 2013, there were ro...
 9.7.60: Use this data for the exercises that follow: In 2013, there were ro...
Solutions for Chapter 9.7: PROBABILITY
Full solutions for College Algebra  1st Edition
ISBN: 9781938168383
Solutions for Chapter 9.7: PROBABILITY
Get Full SolutionsCollege Algebra was written by Patricia and is associated to the ISBN: 9781938168383. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: College Algebra, edition: 1. Since 60 problems in chapter 9.7: PROBABILITY have been answered, more than 9274 students have viewed full stepbystep solutions from this chapter. Chapter 9.7: PROBABILITY includes 60 full stepbystep solutions.

Back substitution.
Upper triangular systems are solved in reverse order Xn to Xl.

Conjugate Gradient Method.
A sequence of steps (end of Chapter 9) to solve positive definite Ax = b by minimizing !x T Ax  x Tb over growing Krylov subspaces.

Diagonalizable matrix A.
Must have n independent eigenvectors (in the columns of S; automatic with n different eigenvalues). Then SI AS = A = eigenvalue matrix.

Dimension of vector space
dim(V) = number of vectors in any basis for V.

Dot product = Inner product x T y = XI Y 1 + ... + Xn Yn.
Complex dot product is x T Y . Perpendicular vectors have x T y = O. (AB)ij = (row i of A)T(column j of B).

Four Fundamental Subspaces C (A), N (A), C (AT), N (AT).
Use AT for complex A.

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

Graph G.
Set of n nodes connected pairwise by m edges. A complete graph has all n(n  1)/2 edges between nodes. A tree has only n  1 edges and no closed loops.

lAII = l/lAI and IATI = IAI.
The big formula for det(A) has a sum of n! terms, the cofactor formula uses determinants of size n  1, volume of box = I det( A) I.

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.

Outer product uv T
= column times row = rank one matrix.

Partial pivoting.
In each column, choose the largest available pivot to control roundoff; all multipliers have leij I < 1. See condition number.

Polar decomposition A = Q H.
Orthogonal Q times positive (semi)definite H.

Positive definite matrix A.
Symmetric matrix with positive eigenvalues and positive pivots. Definition: x T Ax > 0 unless x = O. Then A = LDLT with diag(D» O.

Row space C (AT) = all combinations of rows of A.
Column vectors by convention.

Schwarz inequality
Iv·wl < IIvll IIwll.Then IvTAwl2 < (vT Av)(wT Aw) for pos def A.

Singular Value Decomposition
(SVD) A = U:E VT = (orthogonal) ( diag)( orthogonal) First r columns of U and V are orthonormal bases of C (A) and C (AT), AVi = O'iUi with singular value O'i > O. Last columns are orthonormal bases of nullspaces.

Standard basis for Rn.
Columns of n by n identity matrix (written i ,j ,k in R3).

Wavelets Wjk(t).
Stretch and shift the time axis to create Wjk(t) = woo(2j t  k).
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