Question 4. An engineering firm is constructing power plants at three different sites. Define the events E1, E2, E3 as follows: E1 = the plant at site 1 is completed by the contract date E2 = the plant at site 2 is completed by the contract date E3 = the plant at site 3 is completed by the contract date a) Draw a Venn diagram that depicts these three events as intersecting circles For each scenario (event) described in (b-g) below, draw a new Venn diagram that shades the area of interest and write the event using proper set notation. b) At least 1 plant is completed by the contract date. c) All plants are completed by the contract date. d) None of the plants are completed by the contract date. e) Only the plant at site 1 is completed by the contract date (not E2 and not E3). f) Exactly one of the three plants is completed by the contract date g) Either the plant at site 1 or site 3, or both of the two plants is completed by the contract date (regardless of site 2).
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El = the plant at site 1 is completed by the contract date Ez = the plant at site 2 is completed by the contract date Ez = the plant at site 3 is completed by the contract date Show more…
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Problem 2. Using Venn diagrams, determine which of the following are valid relationships between events. If they are valid, prove the relationship using De Morgan’s laws. (a) (Xc ∡ Y)c = X ∩ Yc (b) Xc ∡ Yc = (X ∡ Y)c (c) (X ∡ Y) ∩ Z = (X ∡ Z) ∩ Y Problem 3. Two dice are tossed and the total number of dots facing up is counted and noted in an experiment. (a) Determine the sample space (b) Find the set A corresponding to the event “ total number of dots is even” (c) Find the set B corresponding to the event “total number of dots is less than 6” (d) Find the set C corresponding to the event “total number of dots is greater than 8” (e) Find Ac, A ∩ B, A ∩ C and B ∩ C (f) Do Ac, B, and C form a partition of the sample space? Explain (g) Assuming that the die is fair find the probabilities of the events A, B and C.
Sri K.
Suppose that a family is leaving on a summer vacation in their camper and M is the event that they will experience mechanical problems, T is the event that they will receive a ticket for committing a traffic violation, and V is the event that they will arrive at a campsite with no vacancies. Referring to the accompanying Venn diagram, list the numbers of the regions that represent the following events. Complete parts (a) through (d) below. The family will experience no mechanical problems and will not receive a ticket for a traffic violation but will arrive at a campsite with no vacancies. (Type a whole number. Use a comma to separate answers as needed.)
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