 8.7.1: Fill in each blank so that the resulting statement is true. Probabi...
 8.7.2: Fill in each blank so that the resulting statement is true. The set...
 8.7.3: Fill in each blank so that the resulting statement is true. The the...
 8.7.4: Fill in each blank so that the resulting statement is true. A stand...
 8.7.5: Fill in each blank so that the resulting statement is true. The pro...
 8.7.6: Fill in each blank so that the resulting statement is true. Because...
 8.7.7: Fill in each blank so that the resulting statement is true. If it i...
 8.7.8: Fill in each blank so that the resulting statement is true. If it i...
 8.7.9: Fill in each blank so that the resulting statement is true. If the ...
 8.7.10: Shown again is the table indicating the marital status of the U.S. ...
 8.7.11: In Exercises 1116, a die is rolled. Find the probability of getting...
 8.7.12: In Exercises 1116, a die is rolled. Find the probability of getting...
 8.7.13: In Exercises 1116, a die is rolled. Find the probability of getting...
 8.7.14: In Exercises 1116, a die is rolled. Find the probability of getting...
 8.7.15: In Exercises 1116, a die is rolled. Find the probability of getting...
 8.7.16: In Exercises 1116, a die is rolled. Find the probability of getting...
 8.7.17: In Exercises 1720, you are dealt one card from a standard 52card d...
 8.7.18: In Exercises 1720, you are dealt one card from a standard 52card d...
 8.7.19: In Exercises 1720, you are dealt one card from a standard 52card d...
 8.7.20: In Exercises 1720, you are dealt one card from a standard 52card d...
 8.7.21: In Exercises 2122, a fair coin is tossed two times in succession. T...
 8.7.22: In Exercises 2122, a fair coin is tossed two times in succession. T...
 8.7.23: In Exercises 2324, you select a family with three children. If M re...
 8.7.24: In Exercises 2324, you select a family with three children. If M re...
 8.7.25: In Exercises 2526, a single die is rolled twice. The 36 equally lik...
 8.7.26: In Exercises 2526, a single die is rolled twice. The 36 equally lik...
 8.7.27: Mega Millions is a multistate lottery played in most U.S. states. ...
 8.7.28: Mega Millions is a multistate lottery played in most U.S. states. ...
 8.7.29: Mega Millions is a multistate lottery played in most U.S. states. ...
 8.7.30: Mega Millions is a multistate lottery played in most U.S. states. ...
 8.7.31: Exercises 3132 involve a deck of 52 cards. If necessary, refer to t...
 8.7.32: Exercises 3132 involve a deck of 52 cards. If necessary, refer to t...
 8.7.33: The table shows the educational attainment of the U.S. population, ...
 8.7.34: The table shows the educational attainment of the U.S. population, ...
 8.7.35: The table shows the educational attainment of the U.S. population, ...
 8.7.36: The table shows the educational attainment of the U.S. population, ...
 8.7.37: The table shows the educational attainment of the U.S. population, ...
 8.7.38: The table shows the educational attainment of the U.S. population, ...
 8.7.39: In Exercises 3944, you are dealt one card from a 52card deck. Find...
 8.7.40: In Exercises 3944, you are dealt one card from a 52card deck. Find...
 8.7.41: In Exercises 3944, you are dealt one card from a 52card deck. Find...
 8.7.42: In Exercises 3944, you are dealt one card from a 52card deck. Find...
 8.7.43: In Exercises 3944, you are dealt one card from a 52card deck. Find...
 8.7.44: In Exercises 3944, you are dealt one card from a 52card deck. Find...
 8.7.45: In Exercises 4546, it is equally probable that the pointer on the s...
 8.7.46: In Exercises 4546, it is equally probable that the pointer on the s...
 8.7.47: Use this information to solve Exercises 4748. The mathematics depar...
 8.7.48: Use this information to solve Exercises 4748. The mathematics depar...
 8.7.49: In Exercises 4952, a single die is rolled twice. Find the probabili...
 8.7.50: In Exercises 4952, a single die is rolled twice. Find the probabili...
 8.7.51: In Exercises 4952, a single die is rolled twice. Find the probabili...
 8.7.52: In Exercises 4952, a single die is rolled twice. Find the probabili...
 8.7.53: If you toss a fair coin six times, what is the probability of getti...
 8.7.54: If you toss a fair coin seven times, what is the probability of get...
 8.7.55: The probability that South Florida will be hit by a major hurricane...
 8.7.56: Describe the difference between theoretical probability and empiric...
 8.7.57: Give an example of an event whose probability must be determined em...
 8.7.58: Write a probability word problem whose answer is one of the followi...
 8.7.59: Explain how to find the probability of an event not occurring. Give...
 8.7.60: What are mutually exclusive events? Give an example of two events t...
 8.7.61: Explain how to find or probabilities with mutually exclusive events...
 8.7.62: Give an example of two events that are not mutually exclusive.
 8.7.63: Explain how to find or probabilities with events that are not mutua...
 8.7.64: Explain how to find and probabilities with independent events. Give...
 8.7.65: The president of a large company with 10,000 employees is consideri...
 8.7.66: In Exercises 6669, determine whether each statement makes sense or ...
 8.7.67: In Exercises 6669, determine whether each statement makes sense or ...
 8.7.68: In Exercises 6669, determine whether each statement makes sense or ...
 8.7.69: In Exercises 6669, determine whether each statement makes sense or ...
 8.7.70: The target in the figure shown contains four squares. If a dart thr...
 8.7.71: Suppose that it is a drawing in which the Powerball jackpot is prom...
 8.7.72: Some threedigit numbers, such as 101 and 313, read the same forwar...
 8.7.73: In a class of 50 students, 29 are Democrats, 11 are business majors...
 8.7.74: On New Years Eve, the probability of a person driving while intoxic...
 8.7.75: a. If two people are selected at random, the probability that they ...
 8.7.76: After a 20% reduction, a digital camera sold for $256. What was the...
 8.7.77: Find the average rate of change of f(x) = x2  1 from x1 = 1 to x2 ...
 8.7.78: Graph f(x) = x2 . Then use the graph of f to obtain the graph of g(...
 8.7.79: Research and present a group report on state lotteries. Include ans...
Solutions for Chapter 8.7: Probability
Full solutions for College Algebra  7th Edition
ISBN: 9780134469164
Solutions for Chapter 8.7: Probability
Get Full SolutionsSince 79 problems in chapter 8.7: Probability have been answered, more than 29105 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: College Algebra , edition: 7. College Algebra was written by and is associated to the ISBN: 9780134469164. Chapter 8.7: Probability includes 79 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions.

Change of basis matrix M.
The old basis vectors v j are combinations L mij Wi of the new basis vectors. The coordinates of CI VI + ... + cnvn = dl wI + ... + dn Wn are related by d = M c. (For n = 2 set VI = mll WI +m21 W2, V2 = m12WI +m22w2.)

Column space C (A) =
space of all combinations of the columns of A.

Covariance matrix:E.
When random variables Xi have mean = average value = 0, their covariances "'£ ij are the averages of XiX j. With means Xi, the matrix :E = mean of (x  x) (x  x) T is positive (semi)definite; :E is diagonal if the Xi are independent.

Cyclic shift
S. Permutation with S21 = 1, S32 = 1, ... , finally SIn = 1. Its eigenvalues are the nth roots e2lrik/n of 1; eigenvectors are columns of the Fourier matrix F.

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.

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).

Elimination matrix = Elementary matrix Eij.
The identity matrix with an extra eij in the i, j entry (i # j). Then Eij A subtracts eij times row j of A from row i.

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

Free columns of A.
Columns without pivots; these are combinations of earlier columns.

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!).

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

Indefinite matrix.
A symmetric matrix with eigenvalues of both signs (+ and  ).

Normal matrix.
If N NT = NT N, then N has orthonormal (complex) eigenvectors.

Orthogonal subspaces.
Every v in V is orthogonal to every w in W.

Pivot.
The diagonal entry (first nonzero) at the time when a row is used in elimination.

Pseudoinverse A+ (MoorePenrose inverse).
The n by m matrix that "inverts" A from column space back to row space, with N(A+) = N(AT). A+ A and AA+ are the projection matrices onto the row space and column space. Rank(A +) = rank(A).

Rotation matrix
R = [~ CS ] rotates the plane by () and R 1 = RT rotates back by (). Eigenvalues are eiO and eiO , eigenvectors are (1, ±i). c, s = cos (), sin ().

Saddle point of I(x}, ... ,xn ).
A point where the first derivatives of I are zero and the second derivative matrix (a2 II aXi ax j = Hessian matrix) is indefinite.

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·

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