 11.7.1: 126 involve probabilities with independent events. Use the spinner ...
 11.7.2: 126 involve probabilities with independent events. Use the spinner ...
 11.7.3: 126 involve probabilities with independent events. Use the spinner ...
 11.7.4: 126 involve probabilities with independent events. Use the spinner ...
 11.7.5: 126 involve probabilities with independent events. Use the spinner ...
 11.7.6: 126 involve probabilities with independent events. Use the spinner ...
 11.7.7: If the pointer is spun three times, find the probability it will la...
 11.7.8: If the pointer is spun three times, find the probability it will la...
 11.7.9: If the pointer is spun three times, find the probability it will la...
 11.7.10: If the pointer is spun three times, find the probability it will la...
 11.7.11: In 1114, a single die is rolled twice. Find the probability of roll...
 11.7.12: In 1114, a single die is rolled twice. Find the probability of roll...
 11.7.13: In 1114, a single die is rolled twice. Find the probability of roll...
 11.7.14: In 1114, a single die is rolled twice. Find the probability of roll...
 11.7.15: In 1520, you draw one card from a 52card deck. Then the card is re...
 11.7.16: In 1520, you draw one card from a 52card deck. Then the card is re...
 11.7.17: In 1520, you draw one card from a 52card deck. Then the card is re...
 11.7.18: In 1520, you draw one card from a 52card deck. Then the card is re...
 11.7.19: In 1520, you draw one card from a 52card deck. Then the card is re...
 11.7.20: In 1520, you draw one card from a 52card deck. Then the card is re...
 11.7.21: If you toss a fair coin six times, what is the probability of getti...
 11.7.22: If you toss a fair coin seven times, what is the probability of get...
 11.7.23: In 2324, a coin is tossed and a die is rolled. Find the probability...
 11.7.24: In 2324, a coin is tossed and a die is rolled. Find the probability...
 11.7.25: The probability that South Florida will be hit by a major hurricane...
 11.7.26: The probability that a region prone to flooding will flood in any s...
 11.7.27: The graph shows that U.S. adults dependent on tobacco have a greate...
 11.7.28: The graph shows that U.S. adults dependent on tobacco have a greate...
 11.7.29: The graph shows that U.S. adults dependent on tobacco have a greate...
 11.7.30: The graph shows that U.S. adults dependent on tobacco have a greate...
 11.7.31: The graph shows that U.S. adults dependent on tobacco have a greate...
 11.7.32: The graph shows that U.S. adults dependent on tobacco have a greate...
 11.7.33: In 3336, we return to our box of chocolates. There are 30 chocolate...
 11.7.34: In 3336, we return to our box of chocolates. There are 30 chocolate...
 11.7.35: In 3336, we return to our box of chocolates. There are 30 chocolate...
 11.7.36: In 3336, we return to our box of chocolates. There are 30 chocolate...
 11.7.37: In 3742, consider a political discussion group consisting of 5 Demo...
 11.7.38: In 3742, consider a political discussion group consisting of 5 Demo...
 11.7.39: In 3742, consider a political discussion group consisting of 5 Demo...
 11.7.40: In 3742, consider a political discussion group consisting of 5 Demo...
 11.7.41: In 3742, consider a political discussion group consisting of 5 Demo...
 11.7.42: In 3742, consider a political discussion group consisting of 5 Demo...
 11.7.43: In 4348, an ice chest contains six cans of apple juice, eight cans ...
 11.7.44: In 4348, an ice chest contains six cans of apple juice, eight cans ...
 11.7.45: In 4348, an ice chest contains six cans of apple juice, eight cans ...
 11.7.46: In 4348, an ice chest contains six cans of apple juice, eight cans ...
 11.7.47: In 4348, an ice chest contains six cans of apple juice, eight cans ...
 11.7.48: In 4348, an ice chest contains six cans of apple juice, eight cans ...
 11.7.49: In 4956, the numbered disks shown are placed in a box and one disk ...
 11.7.50: In 4956, the numbered disks shown are placed in a box and one disk ...
 11.7.51: In 4956, the numbered disks shown are placed in a box and one disk ...
 11.7.52: In 4956, the numbered disks shown are placed in a box and one disk ...
 11.7.53: In 4956, the numbered disks shown are placed in a box and one disk ...
 11.7.54: In 4956, the numbered disks shown are placed in a box and one disk ...
 11.7.55: In 4956, the numbered disks shown are placed in a box and one disk ...
 11.7.56: In 4956, the numbered disks shown are placed in a box and one disk ...
 11.7.57: The table shows the outcome of car accidents in Florida for a recen...
 11.7.58: The table shows the outcome of car accidents in Florida for a recen...
 11.7.59: The table shows the outcome of car accidents in Florida for a recen...
 11.7.60: The table shows the outcome of car accidents in Florida for a recen...
 11.7.61: Shown again is the table indicating the marital status of the U.S. ...
 11.7.62: Shown again is the table indicating the marital status of the U.S. ...
 11.7.63: Shown again is the table indicating the marital status of the U.S. ...
 11.7.64: Shown again is the table indicating the marital status of the U.S. ...
 11.7.65: Shown again is the table indicating the marital status of the U.S. ...
 11.7.66: Shown again is the table indicating the marital status of the U.S. ...
 11.7.67: Shown again is the table indicating the marital status of the U.S. ...
 11.7.68: Shown again is the table indicating the marital status of the U.S. ...
 11.7.69: Shown again is the table indicating the marital status of the U.S. ...
 11.7.70: Shown again is the table indicating the marital status of the U.S. ...
 11.7.71: Shown again is the table indicating the marital status of the U.S. ...
 11.7.72: Shown again is the table indicating the marital status of the U.S. ...
 11.7.73: Probabilities and Coincidence of Shared Birthdays Use a calculator ...
 11.7.74: Explain how to find and probabilities with independent events. Give...
 11.7.75: Explain how to find and probabilities with dependent events. Give a...
 11.7.76: What does P(B A) mean? Give an example
 11.7.77: In 7781, write a probability problem involving the word and whose s...
 11.7.78: In 7781, write a probability problem involving the word and whose s...
 11.7.79: In 7781, write a probability problem involving the word and whose s...
 11.7.80: In 7781, write a probability problem involving the word and whose s...
 11.7.81: In 7781, write a probability problem involving the word and whose s...
 11.7.82: Make Sense? In 8285, determine whether each statement makes sense o...
 11.7.83: Make Sense? In 8285, determine whether each statement makes sense o...
 11.7.84: Make Sense? In 8285, determine whether each statement makes sense o...
 11.7.85: Make Sense? In 8285, determine whether each statement makes sense o...
 11.7.86: If the probability of being hospitalized during a year is 0.1, find...
 11.7.87: If a single die is rolled five times, what is the probability it la...
 11.7.88: Nine cards numbered from 1 through 9 are placed into a box and two ...
 11.7.89: If a single die is rolled twice, find the probability of rolling an...
 11.7.90: Do you live in an area prone to catastrophes, such as earthquakes, ...
 11.7.91: Group members should use the table for 6172 to write and solve four...
Solutions for Chapter 11.7: Events Involving And; Conditional Probability
Full solutions for Thinking Mathematically  6th Edition
ISBN: 9780321867322
Solutions for Chapter 11.7: Events Involving And; Conditional Probability
Get Full SolutionsThis textbook survival guide was created for the textbook: Thinking Mathematically, edition: 6. Thinking Mathematically was written by and is associated to the ISBN: 9780321867322. Chapter 11.7: Events Involving And; Conditional Probability includes 91 full stepbystep solutions. Since 91 problems in chapter 11.7: Events Involving And; Conditional Probability have been answered, more than 71069 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions.

Augmented matrix [A b].
Ax = b is solvable when b is in the column space of A; then [A b] has the same rank as A. Elimination on [A b] keeps equations correct.

Big formula for n by n determinants.
Det(A) is a sum of n! terms. For each term: Multiply one entry from each row and column of A: rows in order 1, ... , nand column order given by a permutation P. Each of the n! P 's has a + or  sign.

CayleyHamilton Theorem.
peA) = det(A  AI) has peA) = zero matrix.

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).

Complex conjugate
z = a  ib for any complex number z = a + ib. Then zz = Iz12.

Diagonal matrix D.
dij = 0 if i # j. Blockdiagonal: zero outside square blocks Du.

Distributive Law
A(B + C) = AB + AC. Add then multiply, or mUltiply then add.

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).

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.

Identity matrix I (or In).
Diagonal entries = 1, offdiagonal entries = 0.

Inverse matrix AI.
Square matrix with AI A = I and AAl = I. No inverse if det A = 0 and rank(A) < n and Ax = 0 for a nonzero vector x. The inverses of AB and AT are B1 AI and (AI)T. Cofactor formula (Al)ij = Cji! detA.

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.

Minimal polynomial of A.
The lowest degree polynomial with meA) = zero matrix. This is peA) = det(A  AI) if no eigenvalues are repeated; always meA) divides peA).

Nullspace N (A)
= All solutions to Ax = O. Dimension n  r = (# columns)  rank.

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.

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 ().

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

Transpose matrix AT.
Entries AL = Ajj. AT is n by In, AT A is square, symmetric, positive semidefinite. The transposes of AB and AI are BT AT and (AT)I.