 10.8.1: Exer. 12: A single card is drawn from a deck. Find the probability ...
 10.8.2: Exer. 12: A single card is drawn from a deck. Find the probability ...
 10.8.3: Exer. 34: A single die is tossed. Find the probability and the odds...
 10.8.4: Exer. 34: A single die is tossed. Find the probability and the odds...
 10.8.5: Exer. 56: An urn contains five red balls, six green balls, and four...
 10.8.6: Exer. 56: An urn contains five red balls, six green balls, and four...
 10.8.7: Exer. 78: Two dice are tossed. Find the probability and the odds th...
 10.8.8: Exer. 78: Two dice are tossed. Find the probability and the odds th...
 10.8.9: Exer. 910: Three dice are tossed. Find the probability of the speci...
 10.8.10: Exer. 910: Three dice are tossed. Find the probability of the speci...
 10.8.11: If three coins are flipped, find the probability that exactly two h...
 10.8.12: If four coins are flipped, find the probability of obtaining two he...
 10.8.13: If , find and .
 10.8.14: If , find and .
 10.8.15: If , find and .
 10.8.16: If , find and .
 10.8.17: Exer. 1718: For the given value of , approximate in terms of X to 1.
 10.8.18: Exer. 1718: For the given value of , approximate in terms of X to 1.
 10.8.19: Four of a kind (such as four aces or four kings)
 10.8.20: Three aces and two kings
 10.8.21: Four diamonds and one spade
 10.8.22: Five face cards
 10.8.23: A flush (five cards of the same suit)
 10.8.24: A royal flush (an ace, king, queen, jack, and 10 of the same suit)
 10.8.25: If a single die is tossed, find the probability of obtaining an odd...
 10.8.26: A single card is drawn from a deck. Find the probability that the c...
 10.8.27: If the probability of a baseball players getting a hit in one time ...
 10.8.28: If the probability of a basketball players making a free throw is 0...
 10.8.29: Exer. 2930: The outcomes of an experiment and their probabilities a...
 10.8.30: Exer. 2930: The outcomes of an experiment and their probabilities a...
 10.8.31: Exer. 3132: A box contains 10 red chips, 20 blue chips, and 30 gree...
 10.8.32: Exer. 3132: A box contains 10 red chips, 20 blue chips, and 30 gree...
 10.8.33: A trueorfalse test consists of eight questions. If a student gues...
 10.8.34: A 6member committee is to be chosen by drawing names of individual...
 10.8.35: Exer. 3536: Five cards are drawn from a deck. Find the probability ...
 10.8.36: Exer. 3536: Five cards are drawn from a deck. Find the probability ...
 10.8.37: Each suit in a deck is made up of an ace (A), nine numbered cards (...
 10.8.38: An experiment consists of selecting a letter from the alphabet and ...
 10.8.39: If two dice are tossed, find the probability that the sum is greate...
 10.8.40: If three dice are tossed, find the probability that the sum is less...
 10.8.41: Assuming that girlboy births are equally probable, find the probab...
 10.8.42: A standard slot machine contains three reels, and each reel contain...
 10.8.43: In a simple experiment designed to test ESP, four cards (jack, quee...
 10.8.44: Three dice are tossed. (a) Find the probability that all dice show ...
 10.8.45: For a normal die, the sum of the dots on opposite faces is 7. Shown...
 10.8.46: In a common carnival game, three balls are rolled down an incline i...
 10.8.47: In an average year during 19951999, smoking caused 442,398 deaths i...
 10.8.48: In a survey about what time people go to work, it was found that 8....
 10.8.49: In a certain county, 2% of the people have cancer. Of those with ca...
 10.8.50: A computer manufacturer buys 30% of its chips from supplier A and t...
 10.8.51: Shown in the figure is a small version of a probability demonstrati...
 10.8.52: In the American version of roulette, a ball is spun around a wheel ...
 10.8.53: In one version of a popular lottery game, a player selects six of t...
 10.8.54: Refer to Exercise 53. The player can win about $1000 for matching f...
 10.8.55: In a quality control procedure to test for defective light bulbs, t...
 10.8.56: A man is 54 years old and a woman is 34 years old. The probability ...
 10.8.57: In the game of craps, there are two ways a player can win a pass li...
 10.8.58: Refer to Exercise 57. In the game of craps, a player loses a pass l...
 10.8.59: (a) Show that the probability p that n people all have different bi...
 10.8.60: Refer to Exercise 59. Find the smallest number of people in a room ...
 10.8.61: Refer to Exercise 57. A player receives $2 for winning a $1 pass li...
 10.8.62: Refer to Exercise 52. If a player bets $1 that the ball will land i...
 10.8.63: A contest offers the following cash prizes: If the sponsor expects ...
 10.8.64: A bowling tournament is handicapped so that all 80 bowlers are equa...
Solutions for Chapter 10.8: Probability
Full solutions for Algebra and Trigonometry with Analytic Geometry  12th Edition
ISBN: 9780495559719
Solutions for Chapter 10.8: Probability
Get Full SolutionsChapter 10.8: Probability includes 64 full stepbystep solutions. This textbook survival guide was created for the textbook: Algebra and Trigonometry with Analytic Geometry, edition: 12. Algebra and Trigonometry with Analytic Geometry was written by and is associated to the ISBN: 9780495559719. Since 64 problems in chapter 10.8: Probability have been answered, more than 35116 students have viewed full stepbystep solutions from this chapter. 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.

Circulant matrix C.
Constant diagonals wrap around as in cyclic shift S. Every circulant is Col + CIS + ... + Cn_lSn  l . Cx = convolution c * x. Eigenvectors in 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.

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].

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!).

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

lAII = l/lAI and IATI = IAI.
The big formula for det(A) has a sum of n! terms, the cofactor formula uses determinants of size n  1, volume of box = I det( A) I.

Left inverse A+.
If A has full column rank n, then A+ = (AT A)I AT has A+ A = In.

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

Multiplication Ax
= Xl (column 1) + ... + xn(column n) = combination of columns.

Network.
A directed graph that has constants Cl, ... , Cm associated with the edges.

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.

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 •

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

Similar matrices A and B.
Every B = MI AM has the same eigenvalues as A.

Spectrum of A = the set of eigenvalues {A I, ... , An}.
Spectral radius = max of IAi I.

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.

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

Tridiagonal matrix T: tij = 0 if Ii  j I > 1.
T 1 has rank 1 above and below diagonal.