A construction firm bids on two different contracts. Let E1 be the event that the bid...
A construction firm bids on two different contracts. Let E1 be the event that the bid on the first contract is successful, and define E2 analogously for the second contract. Suppose that P(E1) = 0.6 and P(E2) = 0.3 and that E1 and E2 are independent events. (a) Calculate the probability that both bids are successful (the probability of the event E1 and E2). (b) Calculate the probability that neither bid is successful (the probability of the event (not E1) and (not E2)). (c) What is the probability that the firm is successful in at least one of the two bids?
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A construction firm bids on two different contracts. Let E1 be
the event that the bid...
Five construction companies each offer bids on three DISTINCT Department of Transportation (DOT) contracts. A particular...
Five construction companies each offer bids on three DISTINCT Department of Transportation (DOT) contracts. A particular company will be awarded at most one DOT contract. a) How many different ways can the bid be awarded? b) Under the assumption that the simple events are equally likely, find the probability that company 2 is awarded a DOT contract. c) Suppose that companies 4 and 5 have submitted non-competitive bids. If the contracts are awarded at random by the DOT, find the...
1. Toss two fair dice and let E1 denote the event that the sum is 10...
1. Toss two fair dice and let E1 denote the event that the sum
is 10 and E2 the event that the first is 3. Show that the two
events are not independent. Construct two independent events.
Construct 4 events that are not independent but such that they are
pairwise independent.
1. Toss two fair dice and let E1 denote the event that the sum is 10 and E2 the event that the first is 3. Show that the two...
A construction firm is currently working on two different buildings. Let denote the event that the...
A construction firm is currently working on two different buildings. Let denote the event that the ith building is completed by the contract date. Use the operations of union, intersection, and complementation to describe each of the following events in terms of A1 and A2and draw a Venn diagram, and shade the region corresponding to each one. 1. At least one building is completed by the contract date Both buildings are completed by the contract date Only the first building...
1. A coustruction firm is working ou two different projects. Let A be the event that...
1. A coustruction firm is working ou two different projects. Let A be the event that the first one is completed by the contract date and defined B atualogously for the second project. (a) Explain the events AUB and An B in words (b) II P(AUB)-0.9 and P(AnB) -0.5, what is the probability that exactly one (Le. not both) is completed by the contract date? Hint: Draw a Venn diagram.)
Firms F1, F2, F3, F4, F5 offer bids on three separate contracts C1, C2, C3. Any...
Firms F1, F2, F3, F4, F5 offer bids on three separate contracts C1, C2, C3. Any firm will be awarded at most one contract. The contracts are such that C1 awarded to F1 is distinguished from C2 to F1. (a) E3 is the event that F3 is awarded a contract. List the elements in E3 and find the probability of E3. (6) E2 is the event that F2 is awarded a contract. List the elements in E2 N E3. Find...
Consider an experiment corresponding to the single throw of a die. Let E1 be the event...
Consider an experiment corresponding to the single throw of a die. Let E1 be the event that the throw is one of 11,2,3,4) and let E2 the event that the throw is one of 13,4,5,6). You are given that P(E) P(E2) 2/3. (a) Identify the smallest o-algebra sf containing the events E1 and E2. (b) Attach probabilities P(J) to all the elements J E (c) What can you say about the probability P(11]) of the event associated to a throw...
2. The contracts for three independent construction jobs are to be assigned to one or more...
2. The contracts for three independent construction jobs are to be assigned to one or more of four competing firms: Firm A, Firm B, Firm C, and Firm D. For each contract, assume that it is equally likely to be awarded to any of the four firms. Let X represent the number of contracts assigned to Firm A, Y the number of contracts assigned to Firm B, and Z the number of contracts assigned to Firm C. (a) Determine the...
Problem 12-18 (Algorithmic) A building contractor is preparing a bid on a new construction project. Two...
Problem 12-18 (Algorithmic) A building contractor is preparing a bid on a new construction project. Two other contractors will be submitting bids for the same project. Based on past bidding practices, bids from the other contractors can be described by the following probability distributions: Contractor Probability Distribution of Bid A Uniform probability distribution between $590,000 and $790,000 B Normal probability distribution with a mean bid of $690,000 and a standard deviation of $49,000 If required, round your answers to three...
An oil exploration company currently has two active projects, one in Asia and the other in...
An oil exploration company currently has two active projects, one in Asia and the other in Europe. Let A be the event that the Asian project is successful and B be the event that the European project is successful. Suppose that A and B are independent events with P(A) = 0.6 and P(B) = 0.7. (a) If the Asian project is not successful, what is the probability that the European project is also not successful? Explain your reasoning.Since the events...
An engineering construction firm is currently working on power plants at three different sites. Let A,...
An engineering construction firm is currently working on power plants at three different sites. Let A, denote the event that the plant at site i is completed by the contract date. Use the operations of union, intersec- tion, and complementation to describe each of the following events in terms of A1, A2, and A3, draw a Venn diagram, and shade the region corresponding to each one. a. At least one plant is completed by the contract 8. , date. b....
1. Toss two fair dice and let E1 denote the event that the sum
is 10 and E2 the event that the first is 3. Show that the two
events are not independent. Construct two independent events.
Construct 4 events that are not independent but such that they are
pairwise independent.
1. Toss two fair dice and let E1 denote the event that the sum is 10 and E2 the event that the first is 3. Show that the two...
A construction firm is currently working on two different buildings. Let denote the event that the ith building is completed by the contract date. Use the operations of union, intersection, and complementation to describe each of the following events in terms of A1 and A2and draw a Venn diagram, and shade the region corresponding to each one. 1. At least one building is completed by the contract date Both buildings are completed by the contract date Only the first building...
1. A coustruction firm is working ou two different projects. Let A be the event that the first one is completed by the contract date and defined B atualogously for the second project. (a) Explain the events AUB and An B in words (b) II P(AUB)-0.9 and P(AnB) -0.5, what is the probability that exactly one (Le. not both) is completed by the contract date? Hint: Draw a Venn diagram.)
Firms F1, F2, F3, F4, F5 offer bids on three separate contracts C1, C2, C3. Any firm will be awarded at most one contract. The contracts are such that C1 awarded to F1 is distinguished from C2 to F1. (a) E3 is the event that F3 is awarded a contract. List the elements in E3 and find the probability of E3. (6) E2 is the event that F2 is awarded a contract. List the elements in E2 N E3. Find...
Consider an experiment corresponding to the single throw of a die. Let E1 be the event that the throw is one of 11,2,3,4) and let E2 the event that the throw is one of 13,4,5,6). You are given that P(E) P(E2) 2/3. (a) Identify the smallest o-algebra sf containing the events E1 and E2. (b) Attach probabilities P(J) to all the elements J E (c) What can you say about the probability P(11]) of the event associated to a throw...
An engineering construction firm is currently working on power plants at three different sites. Let A, denote the event that the plant at site i is completed by the contract date. Use the operations of union, intersec- tion, and complementation to describe each of the following events in terms of A1, A2, and A3, draw a Venn diagram, and shade the region corresponding to each one. a. At least one plant is completed by the contract 8. , date. b....
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