 11.7.1: An ________ is an event whose result is uncertain, and the possible...
 11.7.2: The set of all possible outcomes of an experiment is called the ___...
 11.7.3: To determine the ________ of an event, you can use the formula wher...
 11.7.4: If then is an ________ event, and if then is a ________ event.
 11.7.5: If two events from the same sample space have no outcomes in common...
 11.7.6: If the occurrence of one event has no effect on the occurrence of a...
 11.7.7: The ________ of an event is the collection of all outcomes in the s...
 11.7.8: Match the probability formula with the correct probability name. (a...
 11.7.9: A coin and a sixsided die are tossed.
 11.7.10: A sixsided die is tossed twice and the sum of the results is recor...
 11.7.11: A taste tester has to rank three varieties of yogurt, A, B, and C, ...
 11.7.12: Two marbles are selected (without replacement) from a bag containin...
 11.7.13: Two county supervisors are selected from five supervisors, A, B, C,...
 11.7.14: A sales representative makes presentations about a product in three...
 11.7.15: The probability of getting exactly one tail
 11.7.16: The probability of getting exactly two tails
 11.7.17: The probability of getting a head on the first toss
 11.7.18: The probability of getting a tail on the last toss
 11.7.19: The probability of getting at least one head
 11.7.20: The probability of getting at least two heads
 11.7.21: The card is a face card.
 11.7.22: The card is not a face card.
 11.7.23: The card is a red face card.
 11.7.24: The card is a 9 or lower. (Aces are low.)
 11.7.25: The sum is 6.
 11.7.26: The sum is at least 8.
 11.7.27: The sum is less than 11.
 11.7.28: The sum is 2, 3, or 12.
 11.7.29: The sum is odd and no more than 7.
 11.7.30: The sum is odd or prime.
 11.7.31: Both marbles are red.
 11.7.32: Both marbles are yellow.
 11.7.33: Neither marble is yellow.
 11.7.34: The marbles are of different colors.
 11.7.35: P E 0.87
 11.7.36: P E 0.36
 11.7.37: P 3 E 1 4
 11.7.38: P E 2 P 3
 11.7.39: P E 0.23
 11.7.40: P E 0.92
 11.7.41: P 100 E 17 35
 11.7.42: P E 61 P 100
 11.7.43: GRAPHICAL REASONING In 2008, there were approximately 8.92 million ...
 11.7.44: GRAPHICAL REASONING The educational attainment of the United States...
 11.7.45: GRAPHICAL REASONING The figure shows the results of a recent survey...
 11.7.46: GRAPHICAL REASONING The figure shows the results of a survey in whi...
 11.7.47: DATA ANALYSIS A study of the effectiveness of a flu vaccine was con...
 11.7.48: DATA ANALYSIS One hundred college students were interviewed to dete...
 11.7.49: ALUMNI ASSOCIATION A college sends a survey to selected members of ...
 11.7.50: EDUCATION In a high school graduating class of 128 students, 52 are...
 11.7.51: WINNING AN ELECTION Three people have been nominated for president ...
 11.7.52: PAYROLL ERROR The employees of a company work in six departments: 3...
 11.7.53: PREPARING FOR A TEST A class is given a list of 20 study problems, ...
 11.7.54: PAYROLL MIXUP Five paychecks and envelopes are addressed to five d...
 11.7.55: GAME SHOW On a game show, you are given five digits to arrange in t...
 11.7.56: CARD GAME The deck for a card game is made up of 108 cards. Twenty...
 11.7.57: DRAWING A CARD One card is selected at random from an ordinary deck...
 11.7.58: POKER HAND Five cards are drawn from an ordinary deck of 52 playing...
 11.7.59: DEFECTIVE UNITS A shipment of 12 microwave ovens contains three def...
 11.7.60: PIN CODES ATM personal identification number (PIN) codes typically ...
 11.7.61: RANDOM NUMBER GENERATOR Two integers from 1 through 40 are chosen b...
 11.7.62: RANDOM NUMBER GENERATOR Repeat Exercise 61 for a random number gene...
 11.7.63: FLEXIBLE WORK HOURS In a survey, people were asked if they would pr...
 11.7.64: CONSUMER AWARENESS Suppose that the methods used by shoppers to pay...
 11.7.65: BACKUP SYSTEM A space vehicle has an independent backup system for ...
 11.7.66: BACKUP VEHICLE A fire company keeps two rescue vehicles. Because of...
 11.7.67: ROULETTE American roulette is a game in which a wheel turns on a sp...
 11.7.68: A BOY OR A GIRL? Assume that the probability of the birth of a chil...
 11.7.69: GEOMETRY You and a friend agree to meet at your favorite fastfood ...
 11.7.70: ESTIMATING A coin of diameter is dropped onto a paper that contains...
 11.7.71: If and are independent events with nonzero probabilities, then can ...
 11.7.72: Rolling a number less than 3 on a normal sixsided die has a probab...
 11.7.73: PATTERN RECOGNITION Consider a group of people. (a) Explain why the...
 11.7.74: CAPSTONE
 11.7.75: THINK ABOUT IT A weather forecast indicates that the probability of...
 11.7.76: Toss two coins 100 times and write down the number of heads that oc...
Solutions for Chapter 11.7: Probability
Full solutions for Algebra and Trigonometry  8th Edition
ISBN: 9781439048474
Solutions for Chapter 11.7: Probability
Get Full SolutionsThis textbook survival guide was created for the textbook: Algebra and Trigonometry, edition: 8. Since 76 problems in chapter 11.7: Probability have been answered, more than 51787 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 11.7: Probability includes 76 full stepbystep solutions. Algebra and Trigonometry was written by and is associated to the ISBN: 9781439048474.

Characteristic equation det(A  AI) = O.
The n roots are the eigenvalues of A.

Column picture of Ax = b.
The vector b becomes a combination of the columns of A. The system is solvable only when b is in the column space C (A).

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.

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

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.

Ellipse (or ellipsoid) x T Ax = 1.
A must be positive definite; the axes of the ellipse are eigenvectors of A, with lengths 1/.JI. (For IIx II = 1 the vectors y = Ax lie on the ellipse IIA1 yll2 = Y T(AAT)1 Y = 1 displayed by eigshow; axis lengths ad

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].

Fourier matrix F.
Entries Fjk = e21Cijk/n give orthogonal columns FT F = nI. Then y = Fe is the (inverse) Discrete Fourier Transform Y j = L cke21Cijk/n.

Hessenberg matrix H.
Triangular matrix with one extra nonzero adjacent diagonal.

Markov matrix M.
All mij > 0 and each column sum is 1. Largest eigenvalue A = 1. If mij > 0, the columns of Mk approach the steady state eigenvector M s = s > O.

Multiplier eij.
The pivot row j is multiplied by eij and subtracted from row i to eliminate the i, j entry: eij = (entry to eliminate) / (jth pivot).

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

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

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).

Rank one matrix A = uvT f=. O.
Column and row spaces = lines cu and cv.

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.

Spectral Theorem A = QAQT.
Real symmetric A has real A'S and orthonormal q's.

Toeplitz matrix.
Constant down each diagonal = timeinvariant (shiftinvariant) filter.

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

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.