 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 20814 students have viewed full stepbystep solutions from this chapter. Chapter 9.7: PROBABILITY includes 60 full stepbystep solutions.

Companion matrix.
Put CI, ... ,Cn in row n and put n  1 ones just above the main diagonal. Then det(A  AI) = ±(CI + c2A + C3A 2 + .•. + cnA nl  An).

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

Diagonalization
A = S1 AS. A = eigenvalue matrix and S = eigenvector matrix of A. A must have n independent eigenvectors to make S invertible. All Ak = SA k SI.

Fibonacci numbers
0,1,1,2,3,5, ... satisfy Fn = Fnl + Fn 2 = (A7 A~)I()q A2). Growth rate Al = (1 + .J5) 12 is the largest eigenvalue of the Fibonacci matrix [ } A].

GramSchmidt orthogonalization A = QR.
Independent columns in A, orthonormal columns in Q. Each column q j of Q is a combination of the first j columns of A (and conversely, so R is upper triangular). Convention: diag(R) > o.

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.

Hankel matrix H.
Constant along each antidiagonal; hij depends on i + j.

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

Normal equation AT Ax = ATb.
Gives the least squares solution to Ax = b if A has full rank n (independent columns). The equation says that (columns of A)·(b  Ax) = o.

Nullspace matrix N.
The columns of N are the n  r special solutions to As = O.

Orthonormal vectors q 1 , ... , q n·
Dot products are q T q j = 0 if i =1= j and q T q i = 1. The matrix Q with these orthonormal columns has Q T Q = I. If m = n then Q T = Q 1 and q 1 ' ... , q n is an orthonormal basis for Rn : every v = L (v T q j )q j •

Pascal matrix
Ps = pascal(n) = the symmetric matrix with binomial entries (i1~;2). Ps = PL Pu all contain Pascal's triangle with det = 1 (see Pascal in the index).

Rank r (A)
= number of pivots = dimension of column space = dimension of row space.

Reduced row echelon form R = rref(A).
Pivots = 1; zeros above and below pivots; the r nonzero rows of R give a basis for the row space of A.

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

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

Sum V + W of subs paces.
Space of all (v in V) + (w in W). Direct sum: V n W = to}.

Vector addition.
v + w = (VI + WI, ... , Vn + Wn ) = diagonal of parallelogram.

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

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