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1. A coustruction firm is working ou two different projects. Let A be the event that...
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...
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....
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)...
2. Let A and B be events. Find an expression for the event"exactly one of the...
2. Let A and B be events. Find an expression for the event"exactly one of the events A and B', occurs; simplify your result as far as you can. Draw a Venn diagram for this event.
2. Given events A and B (a) let C be the event that A will occur...
2. Given events A and B (a) let C be the event that A will occur and B will not occur. Express C in terms of A and B. Let D be the event that B will occur and A wil not occur. Express D in terms of A and B (b) let E be the event that exactly one of the events A or B will occur. Express E in terms (c) Use the result in (a) to find...
Exercise 3 (8 marks) Select a Canadian household at random, and let Abe the event that...
Exercise 3 (8 marks) Select a Canadian household at random, and let Abe the event that the selected household is prosperous (income exceeds $85, 000) and B the event that the household is educated (completed college). According to the Census Bureau, P(A)=0.125, P(B)=0.237, and the probability that a household is both prosperous and educated is PIA and B)=0.077. a) What is the probability that the household selected is either prosperous or educated? b) Draw a Venn diagram that shows {A...
3. Section 2.2, Exercise 3 An engineering firm is considering the possibility of establishing a brand...
3. Section 2.2, Exercise 3 An engineering firm is considering the possibility of establishing a brand in Toronto and one in Mexico City. Let T be the event that the firm will cstablish a branch office in Toronto and M be the event that the firm will establish a branch office in Mexico City (a) Express cach of the events described below in terms of set operations on T and M. i. The firm establishes a branch office in both...
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)-0.9 and P(B) 0.s (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 are independent,...
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 8 be the event that the European project is successful. Suppose that A and B are independent events with A)-0.9 and阀8)-0.5 (a) If the Asian project is not successful, what is the probability that the European project is also not successful? Since the events are independent, then A' and B' are...
Let A, B and C be three events defined on a sample space S (for the...
Let A, B and C be three events defined on a sample space S (for the purposes of illustration assume they are not disjoint as shown on the Venn diagram below). Find expressions and draw the Venn diagram for the event, so that amongst A, B and C: a. only A occurs b. both A and B occur, but not C c. all three events occur d. none of the events occurs e. exactly one of the events occurs f....
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...
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....
2. Let A and B be events. Find an expression for the event"exactly one of the events A and B', occurs; simplify your result as far as you can. Draw a Venn diagram for this event.
2. Given events A and B (a) let C be the event that A will occur and B will not occur. Express C in terms of A and B. Let D be the event that B will occur and A wil not occur. Express D in terms of A and B (b) let E be the event that exactly one of the events A or B will occur. Express E in terms (c) Use the result in (a) to find...
Exercise 3 (8 marks) Select a Canadian household at random, and let Abe the event that the selected household is prosperous (income exceeds $85, 000) and B the event that the household is educated (completed college). According to the Census Bureau, P(A)=0.125, P(B)=0.237, and the probability that a household is both prosperous and educated is PIA and B)=0.077. a) What is the probability that the household selected is either prosperous or educated? b) Draw a Venn diagram that shows {A...
3. Section 2.2, Exercise 3 An engineering firm is considering the possibility of establishing a brand in Toronto and one in Mexico City. Let T be the event that the firm will cstablish a branch office in Toronto and M be the event that the firm will establish a branch office in Mexico City (a) Express cach of the events described below in terms of set operations on T and M. i. The firm establishes a branch office in both...
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)-0.9 and P(B) 0.s (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 are independent,...
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 8 be the event that the European project is successful. Suppose that A and B are independent events with A)-0.9 and阀8)-0.5 (a) If the Asian project is not successful, what is the probability that the European project is also not successful? Since the events are independent, then A' and B' are...
Let A, B and C be three events defined on a sample space S (for the purposes of illustration assume they are not disjoint as shown on the Venn diagram below). Find expressions and draw the Venn diagram for the event, so that amongst A, B and C: a. only A occurs b. both A and B occur, but not C c. all three events occur d. none of the events occurs e. exactly one of the events occurs f....
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