 7.5.1: A(n) __________ is a subset of a sample space.
 7.5.2: True or False If E and F are events, sometimes P(E F) = P(E) + P(F).
 7.5.3: True or False If E is an event, then P(E) = 1 + P(E).
 7.5.4: True or False If the odds for an event E are 2 to 1, then P(E) = 1 2 .
 7.5.5: In 512, E and F are events of a sample space S. P(E) = 0.4, P(F) = ...
 7.5.6: In 512, E and F are events of a sample space S. P(E) = 0.6, P(F) = ...
 7.5.7: In 512, E and F are events of a sample space S. P(E) = 0.7, P(F) = ...
 7.5.8: In 512, E and F are events of a sample space S. P(E) = 0.6, P(F) = ...
 7.5.9: In 512, E and F are events of a sample space S. P(F). P(E) = 0.4, P...
 7.5.10: In 512, E and F are events of a sample space S. P(E F) = 0.4, P(F) ...
 7.5.11: In 512, E and F are events of a sample space S. P(E) = 0.4. P(E).
 7.5.12: In 512, E and F are events of a sample space S. P(F) = 0.5 Find P(F).
 7.5.13: Let A and B be events of a sample space S and let and Find the prob...
 7.5.14: Let A and B be events of a sample space S and let and Find the prob...
 7.5.15: Let A and B be two mutually exclusive events of a sample space S. I...
 7.5.16: Let A and B be two mutually exclusive events of a sample space. If ...
 7.5.17: In 1722, determine the probability of E for the given odds 3 to 1 f...
 7.5.18: In 1722, determine the probability of E for the given odds 4 to 1 a...
 7.5.19: In 1722, determine the probability of E for the given odds 7 to 5 a...
 7.5.20: In 1722, determine the probability of E for the given odds 2 to 9 f...
 7.5.21: In 1722, determine the probability of E for the given odds 1 to 1 f...
 7.5.22: In 1722, determine the probability of E for the given odds 50 to 1 ...
 7.5.23: In 2326, determine the odds for and against each event for the give...
 7.5.24: In 2326, determine the odds for and against each event for the give...
 7.5.25: In 2326, determine the odds for and against each event for the give...
 7.5.26: In 2326, determine the odds for and against each event for the give...
 7.5.27: Chicago Bears The Chicago Bears football team has a probability of ...
 7.5.28: Chicago Black Hawks The Chicago Black Hawks hockey team has a proba...
 7.5.29: Likelihood of Passing Anne is taking courses in both mathematics an...
 7.5.30: Dropping a Course After midterm exams, Anne (see 29) reassesses her...
 7.5.31: Car Repair At the Milex tuneup and brake repair shop, the manager ...
 7.5.32: Factory Shortages A factory needs two raw materials, say, E and F. ...
 7.5.33: TV Sets In a survey of the number of TV sets in a house, the follow...
 7.5.34: Supermarket Lines Through observation it has been determined that t...
 7.5.35: 3540 require the following discussion: Blood Types Each of the eigh...
 7.5.36: 3540 require the following discussion: Blood Types Each of the eigh...
 7.5.37: 3540 require the following discussion: Blood Types Each of the eigh...
 7.5.38: 3540 require the following discussion: Blood Types Each of the eigh...
 7.5.39: 3540 require the following discussion: Blood Types Each of the eigh...
 7.5.40: 3540 require the following discussion: Blood Types Each of the eigh...
 7.5.41: Childbirth In 2006, the probability a U.S. woman aged 1544 years, w...
 7.5.42: Tax Returns As of October 31, 2008, 62% of tax refunds for the 2008...
 7.5.43: Bridge Inventory In 2009, there were about 603,000 bridges in the U...
 7.5.44: Trademarks In 2009, there were roughly 352,000 trademark applicatio...
 7.5.45: Apple iPhone Market Share According to the February 2010 Mobile Met...
 7.5.46: Family Cars A family owns two vehicles, a 12yearold Geo Prizm and...
 7.5.47: Patents The number and type of U.S. patents (in thousands) issued i...
 7.5.48: Small Business Loans The number of small business loans awarded to ...
 7.5.49: Mutual Funds A financial consultant estimates that there is a 12% c...
 7.5.50: Airline Travel A poll asked respondents how many air trips they had...
 7.5.51: Track In a track contest the odds that A will win are 1 to 2, and t...
 7.5.52: DUI It has been estimated that in 70% of the fatal accidents involv...
 7.5.53: What is the probability that a sevendigit phone number has one or ...
 7.5.54: What is the probability that a sevendigit phone number contains th...
 7.5.55: Five letters, with repetition allowed, are selected from the alphab...
 7.5.56: Four letters, with repetition allowed, are selected from the alphab...
 7.5.57: Picking Numbers If 30 students are asked to pick a number between 1...
 7.5.58: Picking Numbers If 40 students are asked to pick a number between 1...
 7.5.59: Birthday is the probability that, in a group of 3 people, at least ...
 7.5.60: Birthday is the probability that, in a group of 6 people, at least ...
 7.5.61: Birthday the probability 2 or more U.S. senators have the same birt...
 7.5.62: Birthday the probability 2 or more members of the House of Represen...
 7.5.63: Prove the Additive Rule, Formula (3) on page 394. [Hint: From Examp...
 7.5.64: Prove Equation (5) on page 399. [Hint: If the odds for E are a to b...
 7.5.65: Generalize the Additive Rule by showing the probability of the occu...
 7.5.66: Prove Equation (6) on page 399.
 7.5.67: Thirty students are asked to pick a number between 1 and 60. Ask so...
Solutions for Chapter 7.5: Properties of the Probability of an Event
Full solutions for Finite Mathematics, Binder Ready Version: An Applied Approach  11th Edition
ISBN: 9780470876398
Solutions for Chapter 7.5: Properties of the Probability of an Event
Get Full SolutionsChapter 7.5: Properties of the Probability of an Event includes 67 full stepbystep solutions. Finite Mathematics, Binder Ready Version: An Applied Approach was written by and is associated to the ISBN: 9780470876398. This textbook survival guide was created for the textbook: Finite Mathematics, Binder Ready Version: An Applied Approach, edition: 11. Since 67 problems in chapter 7.5: Properties of the Probability of an Event have been answered, more than 15852 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions.

Adjacency matrix of a graph.
Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected). Adjacency matrix of a graph. Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected).

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.

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

Companion matrix.
Put CI, ... ,Cn in row n and put n  1 ones just above the main diagonal. Then det(A  AI) = ±(CI + c2A + C3A 2 + .•. + cnA nl  An).

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.

Exponential eAt = I + At + (At)2 12! + ...
has derivative AeAt; eAt u(O) solves u' = Au.

Full column rank r = n.
Independent columns, N(A) = {O}, no free variables.

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.

Fundamental Theorem.
The nullspace N (A) and row space C (AT) are orthogonal complements in Rn(perpendicular from Ax = 0 with dimensions rand n  r). Applied to AT, the column space C(A) is the orthogonal complement of N(AT) in Rm.

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

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

Kronecker product (tensor product) A ® B.
Blocks aij B, eigenvalues Ap(A)Aq(B).

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

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.

Positive definite matrix A.
Symmetric matrix with positive eigenvalues and positive pivots. Definition: x T Ax > 0 unless x = O. Then A = LDLT with diag(D» O.

Projection matrix P onto subspace S.
Projection p = P b is the closest point to b in S, error e = b  Pb is perpendicularto S. p 2 = P = pT, eigenvalues are 1 or 0, eigenvectors are in S or S...L. If columns of A = basis for S then P = A (AT A) 1 AT.

Right inverse A+.
If A has full row rank m, then A+ = AT(AAT)l has AA+ = 1m.

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