 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 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 25921 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.

Cramer's Rule for Ax = b.
B j has b replacing column j of A; x j = det B j I det A

Eigenvalue A and eigenvector x.
Ax = AX with x#O so det(A  AI) = o.

Fast Fourier Transform (FFT).
A factorization of the Fourier matrix Fn into e = log2 n matrices Si times a permutation. Each Si needs only nl2 multiplications, so Fnx and Fn1c can be computed with ne/2 multiplications. Revolutionary.

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

Free variable Xi.
Column i has no pivot in elimination. We can give the n  r free variables any values, then Ax = b determines the r pivot variables (if solvable!).

Hermitian matrix A H = AT = A.
Complex analog a j i = aU of a symmetric matrix.

Hypercube matrix pl.
Row n + 1 counts corners, edges, faces, ... of a cube in Rn.

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 .

Independent vectors VI, .. " vk.
No combination cl VI + ... + qVk = zero vector unless all ci = O. If the v's are the columns of A, the only solution to Ax = 0 is x = o.

Inverse matrix AI.
Square matrix with AI A = I and AAl = I. No inverse if det A = 0 and rank(A) < n and Ax = 0 for a nonzero vector x. The inverses of AB and AT are B1 AI and (AI)T. Cofactor formula (Al)ij = Cji! detA.

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

Minimal polynomial of A.
The lowest degree polynomial with meA) = zero matrix. This is peA) = det(A  AI) if no eigenvalues are repeated; always meA) divides peA).

Projection p = a(aTblaTa) onto the line through a.
P = aaT laTa has rank l.

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

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 factorizations A = LDLT and A = QAQT.
Signs in A = signs in D.

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

Unitary matrix UH = U T = UI.
Orthonormal columns (complex analog of Q).

Vector v in Rn.
Sequence of n real numbers v = (VI, ... , Vn) = point in Rn.