 12.3.12.1.118: The ratio of the probability that an event will fail to occur to th...
 12.3.12.1.119: The ratio of the probability that the event will occur to the proba...
 12.3.12.1.120: If the odds in favor of Just in Time winning a horse race are 1 : 3...
 12.3.12.1.121: If the odds against winning at Monopoly are 4 : 1, then the odds in...
 12.3.12.1.122: If the probability that an event will occur is 2 3 then the probabi...
 12.3.12.1.123: If the probability that an event will fail to occur is 1 4 then the...
 12.3.12.1.124: If the odds against an event are 1 : 3, the probability that the ev...
 12.3.12.1.125: If the odds against an event are a to b, then the probability that ...
 12.3.12.1.126: Dressing Up Lila Jaquez is going to wear a blue dress and is trying...
 12.3.12.1.127: Making a Donation In her wallet, Anne Kelly has 12 bills. Six are $...
 12.3.12.1.128: Deal or No Deal In Exercises 11 and 12, consider the TV show Deal o...
 12.3.12.1.129: Deal or No Deal In Exercises 11 and 12, consider the TV show Deal o...
 12.3.12.1.130: Toss a Die In Exercises 1316, a die is tossed. Determine the odds a...
 12.3.12.1.131: Toss a Die In Exercises 1316, a die is tossed. Determine the odds a...
 12.3.12.1.132: Toss a Die In Exercises 1316, a die is tossed. Determine the odds a...
 12.3.12.1.133: Toss a Die In Exercises 1316, a die is tossed. Determine the odds a...
 12.3.12.1.134: Deck of Cards In Exercises 1720, a card is picked from a standard d...
 12.3.12.1.135: Deck of Cards In Exercises 1720, a card is picked from a standard d...
 12.3.12.1.136: Deck of Cards In Exercises 1720, a card is picked from a standard d...
 12.3.12.1.137: Deck of Cards In Exercises 1720, a card is picked from a standard d...
 12.3.12.1.138: Spin the Spinner In Exercises 2124, assume that the spinner cannot ...
 12.3.12.1.139: Spin the Spinner In Exercises 2124, assume that the spinner cannot ...
 12.3.12.1.140: Spin the Spinner In Exercises 2124, assume that the spinner cannot ...
 12.3.12.1.141: Spin the Spinner In Exercises 2124, assume that the spinner cannot ...
 12.3.12.1.142: Students One person is selected at random from a class of 16 men an...
 12.3.12.1.143: Lottery One million tickets are sold for a lottery in which a singl...
 12.3.12.1.144: Billiard Balls In Exercises 2732, use the rack of 15 billiard balls...
 12.3.12.1.145: Billiard Balls In Exercises 2732, use the rack of 15 billiard balls...
 12.3.12.1.146: Billiard Balls In Exercises 2732, use the rack of 15 billiard balls...
 12.3.12.1.147: Billiard Balls In Exercises 2732, use the rack of 15 billiard balls...
 12.3.12.1.148: Billiard Balls In Exercises 2732, use the rack of 15 billiard balls...
 12.3.12.1.149: Billiard Balls In Exercises 2732, use the rack of 15 billiard balls...
 12.3.12.1.150: LPGA Winnings The chart below shows the winnings, in dollars, for t...
 12.3.12.1.151: Rolling a Special Die A special die used in a game contains one dot...
 12.3.12.1.152: Medical Tests The results of a medical test show that of 85 people ...
 12.3.12.1.153: A Red Marble A box contains 9 red and 2 blue marbles. If you select...
 12.3.12.1.154: Scholarship Award The odds in favor of Wendy White winning a schola...
 12.3.12.1.155: Selling a Car The odds in favor of Sam Riveria selling his car are ...
 12.3.12.1.156: College Acceptance The odds against Jason Judd getting accepted int...
 12.3.12.1.157: Winning a Race The odds against Paul Phillips winning the 100 yard ...
 12.3.12.1.158: For example, there are balls marked B1, B2, up to B15; I16, I17, up...
 12.3.12.1.159: For example, there are balls marked B1, B2, up to B15; I16, I17, up...
 12.3.12.1.160: For example, there are balls marked B1, B2, up to B15; I16, I17, up...
 12.3.12.1.161: For example, there are balls marked B1, B2, up to B15; I16, I17, up...
 12.3.12.1.162: For example, there are balls marked B1, B2, up to B15; I16, I17, up...
 12.3.12.1.163: For example, there are balls marked B1, B2, up to B15; I16, I17, up...
 12.3.12.1.164: Blood Types In Exercises 4752, the following circle graph shows the...
 12.3.12.1.165: Blood Types In Exercises 4752, the following circle graph shows the...
 12.3.12.1.166: Blood Types In Exercises 4752, the following circle graph shows the...
 12.3.12.1.167: Blood Types In Exercises 4752, the following circle graph shows the...
 12.3.12.1.168: Blood Types In Exercises 4752, the following circle graph shows the...
 12.3.12.1.169: Blood Types In Exercises 4752, the following circle graph shows the...
 12.3.12.1.170: Fixing a Car Suppose that the probability that a mechanic fixes a c...
 12.3.12.1.171: Diabetes According to the Centers for Disease Control, 8% of Americ...
 12.3.12.1.172: Bookcase Assembly Suppose that the probability that all the parts n...
 12.3.12.1.173: Flight Delays Of 899,000 flights in May 2010, five were delayed on ...
 12.3.12.1.174: Birth Defects Birth defects affect 1 in 33 babies born in the Unite...
 12.3.12.1.175: Odds Against Determine the odds against an even number or a number ...
 12.3.12.1.176: Horse Racing Racetracks quote the approximate odds against each hor...
 12.3.12.1.177: Roulette Turn to the roulette wheel illustrated on page 707. If the...
 12.3.12.1.178: Multiple Births Multiple births make up about 3% of births per year...
 12.3.12.1.179: State Lottery Determine whether your state has a lottery. If so, do...
 12.3.12.1.180: Casino Advantages There are many types of games of chance to choose...
Solutions for Chapter 12.3: Probability
Full solutions for A Survey of Mathematics with Applications  9th Edition
ISBN: 9780321759665
Solutions for Chapter 12.3: Probability
Get Full SolutionsSince 63 problems in chapter 12.3: Probability have been answered, more than 74082 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: A Survey of Mathematics with Applications, edition: 9. A Survey of Mathematics with Applications was written by and is associated to the ISBN: 9780321759665. Chapter 12.3: Probability includes 63 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions.

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

Basis for V.
Independent vectors VI, ... , v d whose linear combinations give each vector in V as v = CIVI + ... + CdVd. V has many bases, each basis gives unique c's. A vector space has many bases!

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.

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

Echelon matrix U.
The first nonzero entry (the pivot) in each row comes in a later column than the pivot in the previous row. All zero rows come last.

Full row rank r = m.
Independent rows, at least one solution to Ax = b, column space is all of Rm. Full rank means full column rank or full row rank.

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.

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

Iterative method.
A sequence of steps intended to approach the desired solution.

Linear transformation T.
Each vector V in the input space transforms to T (v) in the output space, and linearity requires T(cv + dw) = c T(v) + d T(w). Examples: Matrix multiplication A v, differentiation and integration in function space.

Nilpotent matrix N.
Some power of N is the zero matrix, N k = o. The only eigenvalue is A = 0 (repeated n times). Examples: triangular matrices with zero diagonal.

Permutation matrix P.
There are n! orders of 1, ... , n. The n! P 's have the rows of I in those orders. P A puts the rows of A in the same order. P is even or odd (det P = 1 or 1) based on the number of row exchanges to reach I.

Plane (or hyperplane) in Rn.
Vectors x with aT x = O. Plane is perpendicular to a =1= O.

Rayleigh quotient q (x) = X T Ax I x T x for symmetric A: Amin < q (x) < Amax.
Those extremes are reached at the eigenvectors x for Amin(A) and Amax(A).

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.

Schur complement S, D  C A } B.
Appears in block elimination on [~ g ].

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

Solvable system Ax = b.
The right side b is in the column space of A.

Special solutions to As = O.
One free variable is Si = 1, other free variables = o.

Volume of box.
The rows (or the columns) of A generate a box with volume I det(A) I.