Concept explainers
Videos
a.
Find the
a.
Answer to Problem 64CE
The probability of selecting a family that prepared their own taxes is 0.50.
Explanation of Solution
Calculation:
The total number of families is 20 and the number of families prepared their own taxes is 10, the number of families prepared their taxes by a local professional is 7 and the number of families prepared by H&R block is 3.
The probability of selecting a family that prepared their own taxes is obtained as follows:
Thus, the probability of selecting a family that prepared their own taxes is 0.50.
b.
Find the probability that selecting two families, both of which prepared their own taxes.
b.
Answer to Problem 64CE
The probability that selecting two families, both of which prepared their own taxes is 0.2368.
Explanation of Solution
Calculation:
The probability that selecting two families, both of which prepared their own taxes is obtained as follows:
Thus, the probability that selecting two families, both of which prepared their own taxes is 0.2368.
c.
Find the probability of selecting three families, all of which prepared their own taxes.
c.
Answer to Problem 64CE
The probability of selecting three families, all of which prepared their own taxes is 0.1053.
Explanation of Solution
Calculation:
The probability of selecting three families, all of which prepared their own taxes is obtained as follows:
Thus, the probability of selecting three families, all of which prepared their own taxes is 0.1053.
d.
Find the probability that selecting two families, neither of which had their taxes prepared by H&R block.
d.
Answer to Problem 64CE
The probability that selecting two families, neither of which had their taxes prepared by H&R block is 0.7158.
Explanation of Solution
Calculation:
The number of families prepared by H&R block is 3 and the total number of families is 20.
The probability that selecting two families, neither of which had their taxes prepared by H&R block is obtained as follows:
Thus, the probability that selecting two families, neither of which had their taxes prepared by H&R block is 0.7158.
Want to see more full solutions like this?
Chapter 5 Solutions
Statistical Techniques in Business and Economics
- T1.4: Let ẞ(G) be the minimum size of a vertex cover, a(G) be the maximum size of an independent set and m(G) = |E(G)|. (i) Prove that if G is triangle free (no induced K3) then m(G) ≤ a(G)B(G). Hints - The neighborhood of a vertex in a triangle free graph must be independent; all edges have at least one end in a vertex cover. (ii) Show that all graphs of order n ≥ 3 and size m> [n2/4] contain a triangle. Hints - you may need to use either elementary calculus or the arithmetic-geometric mean inequality.arrow_forwardWe consider the one-period model studied in class as an example. Namely, we assumethat the current stock price is S0 = 10. At time T, the stock has either moved up toSt = 12 (with probability p = 0.6) or down towards St = 8 (with probability 1−p = 0.4).We consider a call option on this stock with maturity T and strike price K = 10. Theinterest rate on the money market is zero.As in class, we assume that you, as a customer, are willing to buy the call option on100 shares of stock for $120. The investor, who sold you the option, can adopt one of thefollowing strategies: Strategy 1: (seen in class) Buy 50 shares of stock and borrow $380. Strategy 2: Buy 55 shares of stock and borrow $430. Strategy 3: Buy 60 shares of stock and borrow $480. Strategy 4: Buy 40 shares of stock and borrow $280.(a) For each of strategies 2-4, describe the value of the investor’s portfolio at time 0,and at time T for each possible movement of the stock.(b) For each of strategies 2-4, does the investor have…arrow_forwardNegate the following compound statement using De Morgans's laws.arrow_forward
- Negate the following compound statement using De Morgans's laws.arrow_forwardQuestion 6: Negate the following compound statements, using De Morgan's laws. A) If Alberta was under water entirely then there should be no fossil of mammals.arrow_forwardNegate the following compound statement using De Morgans's laws.arrow_forward
- Characterize (with proof) all connected graphs that contain no even cycles in terms oftheir blocks.arrow_forwardLet G be a connected graph that does not have P4 or C3 as an induced subgraph (i.e.,G is P4, C3 free). Prove that G is a complete bipartite grapharrow_forwardProve sufficiency of the condition for a graph to be bipartite that is, prove that if G hasno odd cycles then G is bipartite as follows:Assume that the statement is false and that G is an edge minimal counterexample. That is, Gsatisfies the conditions and is not bipartite but G − e is bipartite for any edge e. (Note thatthis is essentially induction, just using different terminology.) What does minimality say aboutconnectivity of G? Can G − e be disconnected? Explain why if there is an edge between twovertices in the same part of a bipartition of G − e then there is an odd cyclearrow_forward
Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning