electrical corporation had 2,139,560 electricity customers. Of these, 87% were in the residential area (R); 10.9% were commercial (C); 1.6% were industrial (I); and 0.5% were government (G).These four events (i.e. R, C, I and G) are A. Null events B. Complementary events C. Mutually exclusive events D. Intersection of events

electrical corporation had 2,139,560 electricity customers. Of these, 87% were in the residential area (R); 10.9% were commercial (C); 1.6% were industrial (I); and 0.5% were government (G).These four events (i.e. R, C, I and G) are A. Null events B. Complementary events C. Mutually exclusive events D. Intersection of events

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Consider five mutually exclusive events, V, W, X, Y, and Z, respectively, where P(V) = 0.08, P(W) = 0.43, P(X) = 0.02, P(Y) = 0.41, and P(Z) = .05. What is P(W and X)?
2. Let E and F be events in a sample space S. (a) The probability of E or F occurring is P(E U F) = (b) If the events E and F have no outcome in common (that is, the intersection of E and F is empty), then the events So in drawing a card from a deck, the event E, "getting a heart," and the are called event F, "getting a spade," are , (c) If E and F are mutually exclusive, then the probability of E or F is P(E U F) =
In the city of Savannah, Georgia, 22% of young couples take wedding pictures along the Riverwalk (R), and 42% of young couples take wedding pictures in one of the many historical squares (S) throughout the city. However, only 14% of young couples take wedding pictures along the Riverwalk and in the squares. Are these two events independent of each other? Include the reason why or why not. A. The events aren't independent, because P(R) × P(S) ≠ P(P and S). B. The events are independent, because P(R) × P(S) ≠ P(P and S). C. The events aren't independent, because P(R) × P(S) = P(P and S). D. The events are independent, because P(R) × P(S) = P(P and S)
The following table shows the results of a survey of authors by a (fictitious) publishing company. New Authors Established Authors Total Successful 15 16 31 Unsuccessful 14 2 16 Total 29 18 47 Consider the foilowing events: S: an author is successful; U: an author is unsuccessful; N: an author is new; and E: an author is established. Describe the events N n U and NUU in words. NnU is the event that an author is ( new and unsuccessful NUU is the event that an author is ( either new or unsuccessful Use the table to compute n(N n U) and n(N U U). n(N n U) = 14 n(N U U) = 35
4. 60% of homeowners in Northern Virginia have a weekly lawn service. Those homes with a lawn service, 55% have a sprinkler system. For those without a lawn service, 30% have a sprinkler system. (Note: you do NOT need to simplify these answers. However, you MUST express each in terms of the events/probability notation – e.g., P(A|B) =..) a. Draw a tree diagram to model the problem b. What is the probability that a randomly selected home has a sprinkler system? c. What is the probability that a randomly selected home with a sprinkler system has a lawn service? d. What is the probability that a randomly selected home with a lawn service has a sprinkler system? e. What is the probability that a randomly selected home has a lawn service? f. What is the probability that a randomly selected home that does not have a lawn service has a sprinkler system?
3. Oil exploration : Let D and E be two events in a sample space. It is given that P (D) = 0.4, P (E) = 0.5 and P (DUE) = 0.8. (a) Are the events D and E disjoint? Are the events D and E independent? Then to oil exploration. We imagine two oil fields. The event B = "oil discovery on field 1", while the complementary event B' = "no oil on field 1". Similarly, the event C = "oil discovery on field 2", while C' = "no oil on field 2". We are given that P (B n C) = 0.06, P (B' n C) = 0.12, P (B n C') = 0.11 and P (B' n C') = 0.71. (b) Find the probability of oil on field 1. Assume that oil has been found on field 2. What is now the probability of oil on field 1? Assume that it has been proven that field 2 does not contain oil. What is now the probability of oil on field 1? Are events B and C independent?
A set of 345 college players (graduates and undergraduates) are interviewed by the NFL to play professional football, 240 players graduated from college, of these 190 studied a major in the humanities (history, philosophy, political science, etc.), a total of 95 players (graduates and non-graduates) studied a specialty in applied sciences (administration, engineering, accounting, etc.) of which 45 did not obtain a degree. The following events are defined: Event A -> Humanities Major Player Event A’ -> Player majoring in science Event B -> Graduated Player Event B’ -> Player not graduated Answer the following questions: What is the probability of interviewing a player with a major in the humanities? What is the probability of interviewing a graduate player with a major in the humanities? If a player majoring in the humanities is interviewed, what is the probability that the player has graduated? What is the probability of interviewing a graduated player? What to…
Consider three events A, B, and C. Given- P(A) = 0.3, P(B) = 0.6, P(C) = 0.2, P(A ∩ C) = 0, P(B|C) = 0.5, P(A ∪ B ∪ C) = 0.8 Find P(A ∩ B ∩ C), P(B|C')
1. Geno and Smith collaborated in a Math256 Midterm recently and both received 90 out of a possible 100 points. The events, Geno receiving 90 points and Jason receiving 90 points are : d. All of the answer options are correct.b. disjoint events a. independent events c. dependent events 2. In his Fall Math256 class, 40% of the students studied at least 15 hours per week, 30% of the students received a 4.0, and 10% studied at least 15 hours per week and received a 4.0. Find the probability of students who either studied 15 hours per week or received a 4.0? a. 0.4 d0.7 c. 0.1 b. 0.6 3. Two high school seniors find themselves with much time and nothing to do. They decide to devise a computer game in which a cursor moves randomly along the x axis between 0 and 4. The game they play is to stop the cursor at random points between O and 4 without looking at the screen. Such a game results in a uniform distribution over the interval between 0 and 4 and resembles a density curve. The area…