Probability of Going to Jail in Monopoly

Probability of Going to Jail in Monopoly In the game Monopoly there are a lot of features that involve some aspect of probability. Of course, since the method of moving around the board involves rolling two dice, it is clear that there is some element of chance in the game. One of the places where this is evident is the portion of the game known as Jail. We will calculate two probabilities regarding Jail in the game of Monopoly. Description of Jail Jail in Monopoly is a space in which players can â€Å"Just Visit† on their way around the board, or where they must go if a few conditions are met. While in Jail, a player can still collect rents and develop properties, but is not able to move around the board. This is a significant disadvantage early in the game when properties are not owned, as the game progresses there are times where it is more advantageous to stay in Jail, as it reduces the risk of landing on your opponents’ developed properties. There are three ways that a player can end up in Jail. One can simply land on the â€Å"Go to Jail† space of the board.One can draw a Chance or Community Chest card marked â€Å"Go to Jail.†One can roll doubles (both numbers on the dice are the same) three times in a row. There are also three ways that a player can get out of Jail Use a â€Å"Get out of Jail Free† cardPay $50Roll doubles on any of the three turns after a player goes to Jail. We will examine the probabilities of the third item on each of the above lists. Probability of Going to Jail We will first look at the probability of going to Jail by rolling three doubles in a row. There are six different rolls that are doubles (double 1, double 2, double 3, double 4, double 5, and double 6) out of a total of 36 possible outcomes when rolling two dice. So on any turn, the probability of rolling a double is 6/36 1/6. Now each roll of the dice is independent. So the probability that any given turn will result in the rolling of doubles three times in a row is (1/6) x (1/6) x (1/6) 1/216. This is approximately 0.46%. While this may seem like a small percentage, given the length of most Monopoly games, it is likely that this will happen at some point to someone during the game. Probability of Leaving Jail We now turn to the probability of leaving Jail by rolling doubles. This probability is slightly more difficult to calculate because there are different cases to consider: The probability that we roll doubles on the first roll is 1/6.The probability that we roll doubles on the second turn but not the first is (5/6) x (1/6) 5/36.The probability that we roll doubles on the third turn but not the first or second is (5/6) x (5/6) x (1/6) 25/216. So the probability of rolling doubles to get out of Jail is 1/6 5/36 25/216 91/216, or about 42%. We could calculate this probability in a different way. The complement of the event â€Å"roll doubles at least once over the next three turns† is â€Å"We don’t roll doubles at all over the next three turns.† Thus the probability of not rolling any doubles is (5/6) x (5/6) x (5/6) 125/216. Since we have calculated the probability of the complement of the event that we want to find, we subtract this probability from 100%. We get the same probability of 1 - 125/216 91/216 that we obtained from the other method. Probabilities of the Other Methods Probabilities for the other methods are difficult to calculate. They all involve the probability of landing on a particular space (or landing on a particular space and drawing a particular card). Finding the probability of landing on a certain space in Monopoly is actually quite difficult. This sort of problem can be dealt with by the use of Monte Carlo simulation methods.

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buy custom Social and Economic Change in the Ottoman Empire essay Stuart Schaar and Marvin Gettlemens book the Middle East and the Islamic world reader explores in chapter eleven, the social and economic changes that occurred in the ancient Ottoman Empire. The two authors have incorporated excerpts from the works of three authors to present a detailed anthology of the social and economic transformation of the Ottoman Empire from the fifteenth to the nineteenth century. The first excerpt is from Suraiya Faroqhi. In this excerpt, Suraiya opens the chapter by describing the land tenure system that characterized the Ottoman Empire from the fifteenth to the sixteenth century. Stuart and Marvin then pick up from this except and continue describing the typical land system in the Ottoman Empire Marvin Schaar, (2003) describe the land system as characterized by a farm managed by a peasant family, with additional labor provided by neighbors. The ottoman state owned all the land under its jurisdictions. Peasant farmers were just hereditary peasants who paid some levy to the state for farming this land. People appointed by the central government in the Ottoman Empire were the ones who collected land levies from peasants. In a detailed anthology, Marvin and Stuart, (2003), then explains the contentious issues that characterized the Ottoman Empire land system. They include the conflict over the system of levy collection from peasant farmers, delays in collection of levy by the levy collectors and confusion over the peasants farmers who left their land to look for work in cities. The rural setting presented by Marvin and Stuart of the ancient Ottoman Empire also sheds some good light into the nature of life that ancient Ottoman Empire lived. Most of the people in the Ottoman Empire were peasants and nomadic people who alternated their lifestyles between these two lifestyles. Some of the changes in the land tenure highlighted by Marvin and Stuart in this anthology include a change in the land ownership rights in the sixteenth century. Peasants in the fifteenth century Ottoman Empire had more land rights than the peasants in the sixteenth century onwards because of take over of land by the ruling class that reduced many peasants into laborers. Ottoman Empire largely comprised of a semi agricultural way of life with little divide between town and rural areas. Among the social cultural changes highlighted by Marvin and Stuart, include a growth of mosques in the nineteenth and the early twenty-century and establishments of schools in many towns across the Ottoman Empire. Marvin and Stuat manage to offer a good introduction of the land tenure and the changes that occurred in the land ownership for the period between the fifteenth and the early 20th century. The two authors manage to shed a good light on the complex land tenure of the Ottoman Empire that later brought serious conflicts that eventually led to its collapse. The second excerpt that Marvin and Stuart borrow from is by Hanna Batatu. This excerpt addresses the political changes that occurred in the Ottoman Empire especially the centralization of power by ottoman reformers in many parts of the empire. Some of the effects of the centralization of power are well covered in this excerpts .Examples are strengthening land rights of peasants in some regions of the ottoman empire like the Anatolia region And the aristocrats in Baghdad laying big claims on large tracts of land in Basra depriving the poor of their land. Marvin and Stuart(2003), manages to display in detail the changes that occurred in the ottoman empire when it embraced capitalism influence from western empires like steam navigation, telegraph as a means of communication as well as the political changes such as young Turks revolution in 1908. The two authors also explores in depth how the ottoman imitative of consolidating all land as a property of the state had severe consequences on the balance of power between the different tribes in the ottoman empire and the central government and the levy collectors. In the end, the ottoman initiative of consolidating power eventually led to the strengthening of power of the ruling sheiks against the central government. The sheiks then in an attempt to consolidate power started to lease out land to foreign tribes laying the ground for ethnic tension. With time, many peasants began to resist the authority of the sheiks. Intermixing of tribes occurred that many shaiks lost support of their tribe, which in a way worked towards to their downfall later in the nineteenth century (Marvin Stuart, 2003). Marvin and Stuart expose the major tribal divisions and divisions in the political systems of the Ottoman Empire in this chapter. Their focus is the internal evolution that occurred in the Ottoman Empire through the actions of the peasants, sheiks and the central government. This intriguing historical account of the of complex social economic and political changes that occurred in the ottoman empire and their consequences on the ottoman empire that laid the ground for bitter and bloody divisions within the different tribes and blocs of the empire. Thesee divisions are well presented by Marvin and Stuart as prerequisites for the collapse of the Ottoman Empire in the early 20th century. The third excerpt that Marvin and Stuart (2003), Borrow from Is by Donald Quartet. This excerpt addresses the problem of the slow pace of the industrialization of the ottoman empire Donald attributes the slow pace of industrialization of the ottoman empire to the fact that the ottoman central government favored the agricultural sector more than industrialization . The reason for this preference was that agriculture produce had a ready export market. Marvin and Stuart also explain that the ottoman government did not also encourage industrialists to invest in manufacturing plants in the empire. Other explanations offered by Marvin and Stuart(2003), for slow industrialization in the Ottoman Empire are that the empire preferred to import cheap products from industrialized neighbors than establish industries that would produce its own expensive products. Foreign interference also had an influence in the Ottoman Empire slow pace of industrialization process of the Ottoman Empire .An example is the treaty signed by the Ottoman Empire and Britain that prohibited it from imposing huge duties on imported products. The ottoman empire the fore had no clear policy of protecting its local industries from foreign competition .European Empires interfered with the industrialization process in the ottoman empire to ensure that their products did not face stiff competition from the Ottoman Empire products. As is evident from this detailed presentation by Marvin and Stuart, many external roadblocks prevented the Ottoman Empire from industrialization although there were many laws encouraging the growth of homegrown industries in the Ottoman Empire. The social and economic transformation of the Ottoman Empire was therefore, influenced by interplay of many internal and external factors. Marvin and Stuart manage to give a comprehensive and detailed view of the factors that brought the socio economic changes of the ancient Ottoman Empire and bring into focus the historical, social and economic processes that led to the fall of the Ottoman Empire. Marvin and Stuart have assembled a broad account of the social and the economic transformation of the Ottoman Empire under the influences of factors such as changing social trends, industrialization and European imperialism. This chapter is a great read for people seeking to gain deep insights into the social and economic life of the once mighty Ottoman Empire. Buy custom Social and Economic Change in the Ottoman Empire essay

Genetics Assignment Example | Topics and Well Written Essays - 1250 words - 1

Genetics - Assignment Example Explain: This the coding sequence at any place of the gene and depending on the genetic material that is translocated an entirely new protein will be coded. Missense, point mutation, deletion of 3 bases or nonsense mutation at the end has a less severe effect. As these are all point mutation hence have a smaller influence on the entire structure of the protein. Explain: Cro- Magnon is also referred to as Homo sapien inhabited the earth approximately 10Â  000 to 40Â  000 years ago. This species lived in coexistence with the Neandethals in the Middle East and Europe for many years. The Neanderthal is assumed to have become extinct approximately 33Â  000 years ago. Australopithecus had already faced extinction by the time the Neanderthals came into existence. In addition, since Australopethicus had already become extinct it cannot coexist with homo erectus in the above mentioned time frame. Explain: Sickle cell anaemia is disorder that results from a monogenous disorder that leads to heterogenous clinical presentations. However, the disorder can be considered epistatic due to the fact that the phenotype of the disorder can be influenced by epistatic modifier genes Telomeres have repeated sequences and are located on the endings of each of the chromatids. They serve a protective role at these ends either from deterioration or fusing with the neighbouring chromosomes. In the process of cell division there is degradation of the telomeres which means that the repeated sequences are necessary to ensure that even after this process, there are still other sequences to protect remaining genes. In the Avery MacLeod and MacCathy experiment there were more possibilities and several techniques were utilized attempt to retrieve organic compounds and assess how the inheritance too place. These techniques were not yet present during the Griffith experiment. Griffith utilized heat in his experiment and live strains which