Suppose we have a trlangle made of the 3 vertices A, B, and C, and the 3 edges AB, BC, AC. We color each vertex blue or red uniformly at random. Then define 3 random variables(one for each edge) that Indicate whether the edge's vertices are the same color. Are these three random varlables mutually independent?

Answered: Suppose we have a triangle made of the…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Suppose that 20% of the adult population in Palestine smoke cigarettes only, 15% smoke Argeeleh only, and 10% smoke both cigarettes and Argeeleh. Suppose that 15% of those who smoke cigarettes only have respiratory problems, 10% of those who smoke Agreeleh only have respiratory problems, 20% of those who smoke both cigarettes and Argeeleh have respiratory problems, and 5% of non-smokers have respiratory problems. If an adult person is randomly selected from the population: What is the probability that he/she has respiratory problems? If the selected individual has respiratory problems, what is the probability that he/she is non-smoker? If the selected individual has respiratory problems, what is the probability that he/she smokes both cigarettes and Argeeleh?
5. An office manager is looking to purchase a new printer for his office. He has narrowed his choices down to four printers but cannot decide which of the four he prefers. He has decided to choose two of the four printers at random, and then to let the other members of the office decide which of the two they prefer. The speeds, in pages per minute, of the four printers are 25, 30, 27, and 32. Considering the speeds of the two printers chosen to be the sample, what are the mean and the standard deviation of the sample mean?
Buu has 6 different types (named 1 to 6) of chocolates (in large quantity). Now he plays a game to eat those chocolates. He throws a die (of six sides, non-biased, if the die shows 1, he eats chocolate 1. If the die shows 2, he eats chocolate 2 and so on. Now let X be the number of chocolates of type 1 are eaten and Y be the number of chocolates of type 2 are eaten. What is joint PMF of X and Y ?(Total number of times he roll the die is 4.)
Assume that shoes are produced in three countries: 20 percent in Korea, 40 percent in Canada, and 40 percent in China. At the plant in each country, two types of shoes are made: racing shoes and training shoes. The production at each plant as allocated as shown in the table below. The shoes are randomly distributed to stores in the United States, and you purchase one pair from one of these stores. Plant Racing Training Korea 0.45 0.55 Canada 0.65 0.35 China 0.25 0.75 If you purchase a pair of training shoes selected at random, what is the probability that they were made in Korea?
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The following graph is an interaction plot between factors A and B in a 2* factorial experiment. B+ 60 50 B- 40 B+ 30 20 10 B- Factor A There is a weak interaction between factors A and B Select one: O True O False Response
I need help on both questions. Thank you in advance!
Buu has 6 different types (named 1 to 6) of chocolates (in large quantity). Now he plays a game to eat those chocolates. He throws a die (of six sides, non-biased, if the die shows 1, he eats chocolate 1. If the die shows 2, he eats chocolate 2 and so on. Now let X be the number of chocolates of type 1 are eaten and Y be the number of chocolates of type 2 are eaten. What is joint PMF of X and Y?
You are trying frantically to get dressed, and you need to reach into your sock drawer to get two matching socks in the dark. Your sock drawer contains 20 socks, consisting of 10 matched pairs. All of them are only black or white, and they are loose, disorganized randomly, and not bound together. This means you have 10 black and 10 white socks in your disorganized drawer. This makes 10 total matching pairs of 5 pairs of white and 5 pairs of black. 1. How can you guarantee success of picking a matching pair? In other words, what is the minimum number of socks needing to be picked to guarantee a matching pair? (Hint: There is a right answer to this question!) 2. Explain dependent and independent trials
Read the paper above and answer question # 4 only
A researcher randomly selected 158 personal vehicles and noted the type of vehicle and its color. The two-way table displays the data. A 5-column table with 4 rows. Column 1 has entries sedan, S U V, convertible, total. Column 2 is labeled Red with entries 14, 9, 20, 43. Column 3 is labeled Blue/Green with entries 31, 19, 6, 56. Column 4 is labeled Black/Gray with entries 22, 34, 3, 59. Column 5 is labeled Total with entries 67, 62, 29, 158. The columns are titled Vehicle color and the rows are titled vehicle type. Suppose a vehicle is randomly selected. Let event C = convertible and R = red. What is the value of P(R|C)? StartFraction 29 Over 158 EndFraction StartFraction 43 Over 158 EndFraction StartFraction 20 Over 43 EndFraction StartFraction 20 Over 29 EndFraction
At the beginning of a game of chess, the back row consists of two (identical) rooks on the corners, then two knights next to them, then two bishops, and finally a king and a queen in the center. Bobby Fischer, an American chess legend, popularized the idea of randomly shuffled starting positions. Inhow many distinct ways can the eight pieces above be aligned?

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