University:
California State University, Northridge
Course:
ME 101/L | Introduction to Mechanical Engineering and Lab
Academic year:

2022
Views:

440

Pages:

4
Author:

Sasha Murray

An engineering construction firm is currently working on power plants at three different sites. Define events E1 , E2 , and E3 as follows The following Venn diagram pictures the relationships among these events: Shade the region in the Venn diagram corresponding to each of the following events. Redraw the Venn diagram for each part of the problem. (Hint: See the discussion of Venn diagrams) At least one plant is completed by the contract date. Answer This remark suggests that at least one plant at one of the three locations will be finished by the contract date. We can rephrase this to imply that the plant is completed by the contract date at site 1, site 2, or site 3. The shading in Figure below illustrates this better. Here is a graphical depiction of the solution. A1=the completion of the plant at Site 1 by the contract date. A2=the completion of the plant at Site 2 by the contract date. A3=the completion of the plant at Site 3 by the contract date. S stands for sample space (the set of all possible outcomes ) A1 U A2 U A3 All plants are completed by the contract date. Answer According to the issue, all plants are completed by the contract date. This means that we're seeking for the set of outcomes that are present in all three occurrences, A1, A2, and A3. In other words, we may state the plant is finished at sites 1, 2, and 3, suggesting that we should utilise intersections to depict the occurrence. The shaded region in Figure below covers the location where the three events intersect, i.e., where they all occur. A1 n A2 n A3 None of the plants are completed by the contract date. Answer (A1 n A2 n A3)’ Only the plant at Site 1 is completed by the contract date. Answer Event A1 happens in this sentence, but not A1 with another event A2 or A3. This event can be thought of as all conceivable outcomes excluding events A2 and A3. In terms of probability, all of the possibilities in the sample space, including event A1, with the exception of events A2 and A3. This occurrence is depicted in Figure by the darkened region. The event can be symbolically represented by the intersection of event A1 with the complements of events A2 and A3: A1 n A2' n A3' Exactly one of the three plants is completed by the contract date. Answer This phrase implies that just one of the occurrences takes place. None of the outcomes with multiple events may be included. This event is depicted in Figure as the outcomes of the three events that do not overlap with any of the results of other events. This event may be represented using unions, intersections, and complements. (A1 n A2' n A3') U (A1' n A2 n A3') U (A1' n A2' n A3') Either the plant at Site 1 or both of the other two plants are completed by the contract date. Answer This issue may be rewritten to state all potential outcomes that are either in event A1 or in events A2 and A3. As seen in Figure , this region comprises the consequences of event A1 as well as the outcomes of the intersection of events A2 and A3. This event may be defined as A1 in union with the intersection of A2 and A3: A1 U (A2 n A3)