How to Calculate Powerball Odds

How to Calculate Powerball Odds Powerball is a multistate lottery that is quite popular due to its multimillion-dollar jackpots. Some of these jackpots reach values that are well over $100 million. An interesting quest ion from a probabilistic  sense is, â€Å"How are the odds calculated on the likelihood of winning Powerball?† The Rules First we will examine the rules of Powerball as it is currently configured. During each drawing, two drums full of balls are thoroughly mixed and randomized. The first drum contains white balls numbered 1 to 59. Five are drawn without replacement from this drum. The second drum has red balls that are numbered from 1 to 35. One of these is drawn. The object is to match as many of these numbers as possible. The Prizes The full jackpot is won when all six numbers selected by a player match perfectly with the balls that are drawn. There are prizes with lesser values for partial matching, for a total of nine different ways to win some dollar amount from Powerball. These ways of winning are: Matching all five white balls and the red ball wins the grand prize jackpot. The value of this varies depending upon how long it has been since someone has won this grand prize.Matching all five white balls but not the red ball wins $1,000,000.Matching exactly four of the five white balls and the red ball wins $10,000.Matching exactly four of the five white balls but not the red ball wins $100.Matching exactly three of the five white balls and the red ball wins $100.Matching exactly three of the five white balls but not the red ball wins $7.Matching exactly two of the five white balls and the red ball wins $7.Matching exactly one of the five white balls and the red ball wins $4.Matching just the red ball but none of the white balls wins $4. We will look at how to calculate each of these probabilities. Throughout these calculations, it is important to note that the order of how the balls come out of the drum is not important. The only thing that matters is the set of balls that are drawn. For this reason our calculations involve combinations and not permutations. Also useful in every calculation below is the total number of combinations that can be drawn. We have five selected from the 59 white balls, or using the notation for combinations, C(59, 5) 5,006,386 ways for this to occur. There are 35 ways to select the red ball, resulting in 35 x 5,006,386 175,223,510 possible selections. Jackpot Although the jackpot of matching all six balls is the most difficult to obtain, it is the easiest probability to calculate. Out of the multitude of 175,223,510 possible selections, there is exactly one way to win the jackpot. Thus the probability that a particular ticket wins the jackpot is 1/175,223,510. Five White Balls To win $1,000,000 we need to match the five white balls, but not the red one. There is only one way to match all five. There are 34 ways to not match the red ball. So the probability of winning $1,000,000 is 34/175,223,510, or approximately 1/5,153,633. Four White Balls and One Red For a prize of $10,000, we must match four of the five white balls and the red one. There are C(5,4) 5 ways to match four of the five. The fifth ball must be one of the remaining 54 that were not drawn, and so there are C(54, 1) 54 ways for this to happen. There is only 1 way to match the red ball. This means that there are 5 x 54 x 1 270 ways to match exactly four white balls and the red one, giving a probability of 270/175,223,510, or approximately 1/648,976. Four White Balls and No Red One way to win a prize of $100 is to match four of the five white balls and not match the red one. As in the previous case, there are C(5,4) 5 ways to match four of the five. The fifth ball must be one of the remaining 54 that were not drawn, and so there are C(54, 1) 54 ways for this to happen. This time, there are 34 ways to not match the red ball. This means that there are 5 x 54 x 34 9180 ways to match exactly four white balls but not the red one, giving a probability of 9180/175,223,510, or approximately 1/19,088. Three White Balls and One Red Another way to win a prize of $100 is to match exactly three of the five white balls and also match the red one. There are C(5,3) 10 ways to match three of the five. The remaining white balls must be one of the remaining 54 that were not drawn, and so there are C(54, 2) 1431 ways for this to happen. There is one way to match the red ball. This means that there are 10 x 1431 x 1 14,310 ways to match exactly three white balls and the red one, giving a probability of 14,310/175,223,510, or approximately 1/12,245. Three White Balls and No Red One way to win a prize of $7 is to match exactly three of the five white balls and not match the red one. There are C(5,3) 10 ways to match three of the five. The remaining white balls must be one of the remaining 54 that were not drawn, and so there are C(54, 2) 1431 ways for this to happen. This time there are 34 ways to not match the red ball. This means that there are 10 x 1431 x 34 486,540 ways to match exactly three white balls but not the red one, giving a probability of 486,540/175,223,510, or approximately 1/360. Two White Balls and One Red Another way to win a prize of $7 is to match exactly two of the five white balls and also match the red one. There are C(5,2) 10 ways to match two of the five. The remaining white balls must be one of the remaining 54 that were not drawn, and so there are C(54, 3) 24,804 ways for this to happen. There is one way to match the red ball. This means that there are 10 x 24,804 x 1 248,040 ways to match exactly two white balls and the red one, giving a probability of 248,040/175,223,510, or approximately 1/706. One White Ball and One Red One way to win a prize of $4 is to match exactly one of the five white balls and also match the red one. There are C(5,4) 5 ways to match one of the five. The remaining white balls must be one of the remaining 54 that were not drawn, and so there are C(54, 4) 316,251 ways for this to happen. There is one way to match the red ball. This means that there are 5 x 316,251 x1 1,581,255 ways to match exactly one white ball and the red one, giving a probability of 1,581,255/175,223,510, or approximately 1/111. One Red Ball Another way to win a prize of $4 is to match none of the five white balls but match the red one. There are 54 balls that are not any of the five selected, and we have C(54, 5) 3,162,510 ways for this to happen. There is one way to match the red ball. This means that there are 3,162,510 ways to match none of the balls except for the red one, giving a probability of 3,162,510/175,223,510, or approximately 1/55. This case is somewhat counterintuitive. There are 36 red balls, so we may think that the probability of matching one of them would be 1/36. However, this neglects the other conditions imposed by the white balls. Many combinations involving the correct red ball also include matches on some of the white balls as well.

Nissan Altima Electric Mode Hybrid Car Question

Nissan Altima Electric Mode Hybrid Car Question Hello Christine and Scott, I was very relieved to find your pages under About.com and find out I could email you. A few weeks ago we purchased a 2008 Nissan Altima Hybrid and recently we noticed something that has us worried: the gasoline engine kicks on a few seconds after starting the car and while the car is still in PARK. It stays on EV MODE for only the first few seconds. This is not what we expected! We thought (from research) that the high voltage battery would have total control at startup, low speeds, and when not moving (at a stop sign /red light). In other words, NO GASOLINE being used at these times. EV MODE the whole time! We also observed: 1. After we shift to D, DRIVE, it happens again every time the vehicle comes to a full stop while at a stop sign or red light and were not moving for more than a few seconds. 2. The engine stays on for at least a minute and then shuts off, EV MODE resumes and all is quiet until I start moving and accelerating. 3. This behavior seems to happen when the engine is cold, in other words, when it hasnt been used for hours (e.g. first drive in the morning) and keeps happening for about 1/2 hour or so during that first drive. After 1/2 hour or so, this stops happening. In other words, the EV MODE sign comes on and STAYS ON the whole time the car is stopped (idle) at a stop sign/red traffic light or while the car is in PARK but still on. This is what we thought would ALWAYS happen! 4. There is one exception to what I just said in item 3 above. Today for the first time, while at a red light, and after the car went into EV MODE, the engine kicked on even though I had just driven the car for at least one hour at high speeds on highway. Is something wrong with my car? I noticed on your website that you own your own 2008 Nissan Hybrid. Please tell me whats happening with yours. At first my husband thought that this was due to the cold weather (under 40 degrees). But today, the temperature was at 48 degrees and it still didnt stay in EV MODE at startup. Please help. I am afraid this might be a defective car. Dora PS. Yesterday I drove the car to the dealer and the salesperson that sold us the car told us that he has seen it happen before and that it is normal. He even had me drive another hybrid (2007) that had not been sold yet and sure enough, seconds after the car started, the EV MODE signal disappeared and the engine started EVEN THOUGH I was still in park mode. I dont know whether to believe him or not. I also dont find any info on manual to either identify this behavior as normal or not normal. Hey Dora, Thanks for writing - good questions. We understand your concerns. No worries – it sounds as if your 2008 Altima Hybrid is working perfectly normally. Your husband is right - it does have a lot to do with the cold temperatures, and there actually are several conditions that will make the engine on your car run, regardless of your input. They are: State of battery charge Temperature of the engine and hybrid components Ambient air temperature When you start the car, it will usually start the engine after just a few seconds, even if its been only a few hours since youve last driven it. The computer does this automatically to warm the engine, hybrid battery and associated hybrid components. Under mild weather conditions, the engine should shut off after just a few minutes, but when it’s colder out, it could take substantially longer- it also depends upon the amount of charge left in the hybrid battery. If it’s on the low side, the engine may continue running to charge the battery up to full capacity. Also, and this is especially true in the winter (and if you are using the heater and/or the defroster a lot), the engine will run longer. The engine has to run to warm the cabin- and the higher you have the heat set (and the longer it’s on), the more the engine will run. If you have electrically heated seats, using those can help minimize the need to heat the cabin air as much, thus minimizing the engine ru nning time also. Even if you are stopped for a minute or more at a traffic light and the car is in EV mode, if any of these conditions come up (low battery, car needing heat), the engine will start. Again, all of this is normal. You’ll notice as we get into spring and early summer (and you won’t be needing the heat/defroster as much), everything will come up to operating temperature quicker and the Altima Hybrid will stay in EV mode much longer. In the summertime when it gets really hot and you’re using the AC a lot, you could notice that it runs the engine more. The AC compressor runs off electricity, so you may find the engine kicks on more often to keep the battery charged. Just bear in mind that this is a hybrid electric car and is reliant upon the gasoline engine to keep the entire system up and running. Even though you can drive in electric mode, it’s still more of an assistant than a main power source. Your Altima uses Toyota’s Synergy Drive System- in our opinion, it is the best one available. As you get used to this car, we bet you’ll not only be able to maximize the EV mode driving (and fuel economy), but come to love it as well. For your reference, here’s an article we wrote about hybrids and cold temps, and some info about obtaining the best mileage from your hybrid via hypermiling. (Yep, Scott hypermiled in the Altima Hybrid- look what it can do. Thanks for visiting our site and writing- please feel free to let us know if you have any more questions. Best regards, Christine Scott

To what extent do you agree with the view that HRM is probably the Essay

To what extent do you agree with the view that HRM is probably the most culturally sensitive of all managerial functional areas - Essay Example Furthermore, an organization’s socio-cultural environment affects the adaptation of Human Resource Management Strategies and different cultural contexts pose different challenges. For firms doing business in multicultural environments or generally across cultures parochial views to management of human resources can proof disastrous. This paper looks into the strong interrelationship that exists between Human Resource Management (HRM) and people’s culture. Theories that have been developed to explain the phenomenon are also to be explored. Today’s business environment has taken a turn to be one that is highly globalised meaning that a firm operating in a certain area or country, it does not necessarily expect to have people of that area only or even that country alone (Lawson & Shen 1998). This therefore stipulates that such kind of an organization should expect to have a workforce that is multiethnic or exhibiting variations in cultural backgrounds. This hereby calls for the HR Manager or the management to embrace this fact so as to ensure survival in the increasingly competitive and volatile global business environment. Just but to give an example is the tendency where firms from the developed countries set camp in developing countries and move ahead to adopt standard HRM approaches to their new workforce. This kind of approach tends to undermine the cultural reality of the people and these strategies before long crumble to the management’s amazement. This not withstanding, knowledge of the target mark et’s culture is essential in ensuring a firm’s survival. Culture in this regard is the collective social occurrence that goes on to affect the HRM practices in an organization operating in a particular cultural context. A culture of a people is a phenomenon that cannot be changed due to the fact that it has been with them for a long time and that they identify themselves with it. Culture in this respect gives one their

Impact of Industrialization on the National Business Systems and the Essay

Impact of Industrialization on the National Business Systems and the National Competitiveness - Essay Example To understand the questions completely, each of the fundamental terminologies which are to have an impact on the final question needs to be addressed and needs to be linked to the main question in pursuit. INDUSTRIALIZATION: The early phase of industrialization was from 1750 to the 1800s.Although, it can be debated over the exact timings of the industrialization in the different parts of the world, but it was the above mentioned period during which industrialization emerged in its totality. Europe in general and Britain in particular was the main element in crafting the early period of industrialization (Henderson, 1954). Until then, work was majorly done using manual labor and the amount of production, as a result, was squat. But it was end of the 18th century which actually saw the revolution in production processes and changed the dynamics of production and industry concepts. Enhanced use of machine-driven principles, including steam power, to develop in Great Britain produced an identifiable change in economic structure and growth (Spielvogel, 2011). The period saw the emergence of factory system where workers were grouped together and capital structures changed from the earlier used methods to cost effective technology driven methods. Cotton and iron were the key dynamics in this course (Thomas, 1964). Cotton was earlier processed through manual labor which tool time and effort but did not produce in mass volume. The production capacity was low and thus, the efficiency was significantly less. But now machines were developed which were, at first, powered by water and later on, with thw advancement in the system, by steam, and which now increased the production immensely. The number of people employed naturally increased. Moreover, the new process caused the cost of the final products to sharply decrease making them competitive. It was vital for Britain to acquire the new technology. It helped Britain to cement its dominance on the worlds economical and the resulting political sphere (Henderson, 1954). It took little time for industrialization to travel from Britain to the rest of the western world. It can be said that industrialization did not take more than fifty years to travel from Britain to the rest of the western world including America. But it has taken time to encompass the eastern boundaries. This statement is essential to understand because it has been one of the fundamental differences between the eastern and the western world.The eastern world could not be the recipient of the process of industrialization because its majority was under the colony system of one or more of the European countries. United States of America became a grateful receiver of the new dynamics in the production processes. The concept of corporations emerged whereby the people were given the new concept of working in huge setups and in a pronounced number of people.Because of the complexity of the new organization setup, several theories and ways of ef ficiently working in corporations were also developed. The early phase saw the owners of the corporations to receive the greatest benefit out of the sales and the workers in these firms to suffer the low wage rates and pitiable working conditions (Wilensky, 1965). It was natural for this phenomenon to take toll. This is because it was the part of the evolution through which the countries had to go in order to accept the new paradigm of industrializat

An Inspector Calls by J.B. Priestley :: Papers

An Inspector Calls by J.B. Priestley In my English class I have been reading the play 'An Inspector Calls'! The play is about a fairly well-off family (the Birling's) who have their evening spoilt by having an inspector call round, to ask them questions about a girl, Eva Smith, who drank some disinfectant to kill herself. I am going to start my comparisons with the head of the house-hold, Arthur Birling. Arthur Birling is a selfish, arrogant, family man who doesn't know the meaning of the word responsibility. The play starts off with the family sat around the dining table, toasting to the daughter, Sheila's, engagement to Gerald Croft. While the girls (Sheila and her mother, Sybil) trail off to the drawing room, Arthur decides to teach Gerald something about responsibility; 'A man has to mind his own business and look after himself and his own' He also has a fairly good reason as to why he thinks like this, and he tells so to the inspector; 'If we were all responsible for everything that happened to everybody we'd had anything to do with, it would be very awkward, wouldn't it?' When Arthur doesn't know the full story as to why the inspector has arrived, he tries to use his importance to get his way. He threatens the inspector with the following phrase; 'I've half a mind to report youà ¢Ã¢â€š ¬Ã‚ ¦ perhaps I ought to warn you thatà ¢Ã¢â€š ¬Ã‚ ¦ our chief constableà ¢Ã¢â€š ¬Ã‚ ¦ he's an old friend of mine, and that I see him fairly often' Arthur doesn't react at all to the death of Eva, and he acts as though 'such is life'. When the inspector leaves towards the end of the play, Arthur tries to think of all sorts of idea's to prove that the man wasn't an inspector at all, - proving that Arthur didn't change at all in reaction to the death of one of his former employees. Sybil Birling is Arthur's wife. She is very like her husband in being selfish, and is very unrepentant. Sybil finds out that she had

Les Demoiselles D’avignon Essay

My museum paper is on the Les Demoiselles d’Avignon, painted by Pablo Picasso in Paris, June-July 1907. Oil on canvas, 8’x7’ 8† (243.9Ãâ€"233.7cm). He became one of the greatest and most influential artists of the 20th century and the creator (with Georges Braque) of Cubism. A Spanish painter, sculptor, printmaker, ceramicist, and stage designer, Picasso was considered radical in his work. Born October 25, 1881, Malaga, Spain, and after a long prolific career, he died April 8, 1973 in Mougins, France. This was my first time at the Museum of Modern Art; I never went there because I never had everyone to go with me. I went with my cousin; she is an art teacher and who better to go to the Museum of Modern Art with then an art teacher. When we first got to the museum there wasn’t much to see in the lobby. We went on the escalator to the fifth floor were hundreds of people walking all thought-out the galleries. My cousin explained all the different types of art and artists to me as we were walking though the galleries. I ended up in the Alfred H. Barr Jr. Painting and Sculpture Galleries where I seen a painting from a French painter, Fernand Leger called â€Å"Women with a Book† I thought that was the painting that I wanted to do my report on, but when I seen art work from Pablo Picasso like, The Studio, Ma Jolie and The Three Musician I was speechless. Some of his work that I seen at the museum was breathtaking, but one in particular caught my eye; it was the Les Demoise lles d’Avignon. It is located in the Blanchette Hooker Rockefeller, Second Gallery. As you walk into the gallery, the â€Å"Les Demoiselles d’Avignon† is the first painting you see, because of how large it is, and all the bright colors in the art work. When I seen the Les Demoiselles d’Avignon in my art book I through that it was a nice painting, but when I stood right in-front of it I was astonish. The Les Demoiselles d’Avignon is not just a painting; it truly is a master piece. There had to be about thirty people standing around the Les Demoiselles d’Avignon and another twenty people looking at the other art work in the room. Some people were just standing looking at the painting, some taking pictures. As I, started taking pictures of Les Demoiselles d’Avignon I couldn’t help but notice the painting to the right, it was called â€Å"Repose† and to the left was another painting called the â€Å"Two Nudes† both are painted by Picasso. Les Demoiselles d’Avignon are the woman of Avignon, the term demoiselles (meaning â€Å"young ladies†), was a euphemism for prostitutes and â€Å"Avignon† refers not to the French town but to a street in the red-light district of the city of Barcelona where Picasso was a young artist. (Art A Brief History), pg 532. Print. The d’Avignon are actually five prostitutes, and these are five women naked. They’re looking at us, as much as we’re looking at them. The very early studies show a sailor walking into this curtained room where the ladies stand and the woman on the far left now has the traces of having been that man entering the room, and you can even feel a certain masculinity in the sort of sculptural carving of her body and the way that the very large foot is stepping toward the others. It almost seem like it’s a build-up of geometric forms, and if you look at the chest of the woman at the very top right, you can see one of these cubes making up the space underneath her chin, thus the name Cubism. One striking aspect of this painting is the way that it’s staged on which these women are painted, is almost looming out at the viewer. Rather than feeling like these woman are nice and safely set back in some kind of room, that you are peering into. I feel like the woman are almost piled on top of each other. Piled in such a way that the canvas is almost stepping out at the viewer. Its part of the desire of the painting to confront you, I think physically, psychologically, as well as intellectually with everything that’s going on in it. It’s painted in pinkish, peach flesh skin tones against a back drop of brown, white and blue curtains. The figures are very flat and theirs is little illusion that these are real bodies. Looking at the five figu res from left to right, the woman to the far left is standing in profile facing right with her left hand; she reaches up behind her head to hold an orange brown curtain back. She has long straight black hair falling down her back. Her head, from the neck up peers to be in shadow or sun-tan, it’s a darker brown than the pinkish flesh of her body. She stares straight ahead expressionless. Her right eye from the front view is large, simplified and out-lined in black with a black pupil surrounded by brown. Her right arm hangs stiffly by her side. Her breast jets forward in a ruff square shape. Beside this figure, in the center of this painting are two women looking directly forward, straight out of the canvas. Their black eyes are wide and uneven. Their left eye brows extend a sweeping line to form simplify noses. Their mouths are straight lines. The one on the left raises her bent right elbow and places her hand behind her head, as if posing seductively. Her black hair is pulled back and falls behind her left shoulder. Her breasts are half circles; none of the women’s breast has nipples. The women on the right, raises both arms and puts both hands behind her hand. Her dark brown hair is pulled into a high bun. The last two figures don’t fit in with the painting, they are unexpected. The one to the top right stands back, her raised arms parting the blue curtain on which she’s coming out from. Her black hair hangs down her back; one eye socket black and empty. Her nose, like her face is large and elongated, striped diagonally in green across her cheek, suggesting less the face of a human then the forms of an African mask. In front of her, is another woman she is sitting or squatting, elbow on one raised knee which jets forward at the center of the painting almost looks as if her back is facing the viewer, but that is not true because her dark tan face is turned towards the viewer. She raises her arm to her face and beneath her chin is a large ambiguous form recalling a boomerang, it might be her hand, or a piece of melon she’s eating. Her body is flat and her nose is also stripped. Her face looks like a mask, and she has one uneven eye completely white, the other completely blue. The drapery behind them doesn’t hang softly; it looks like shatter pieces of glass with blue and white tones. In the center at the bottom of the painting are assorted fruits on a wrinkle white cloth; a pear, an apple, grapes and a slice of melon. The pear and apple have shrieks of red in them, the melon is reddish too and the grapes are grayish white. In conclusion, my experience at the Museum of Modern Art was delightful. Walking through the museum and seeing ancient statues and painting from so many different decades was so fulfilling. I didn’t realize how much I enjoy looking at art work; I just wanted to see more and more. I kept asking myself, how did they do this? How did they do that? What were they thinking when they paint this? Even though I didn’t get all my answers I was like a sponge, soaking it all up. What a wonderful, amazing day. I will definitely go back. Bibliography: Cothren Michael W., and Marilyn Stokstad. Art: A Brief History 4th ed. Page.531, 19-7. Acquired through the Lillie P. Bliss Bequest (333.1939) Laurence King Publishing Ltd, London. (2010-2007) Print. Museum of Modern Art 11 West 53 Street, New York, NY 10019. April 29, 2012 Pablo Picasso. Les Demoiselles d’Avignon. 1907. Oil on canvas, 8†² x 7†² 8†³ (243.9 x 233.7 cm). Acquired through the Lillie P. Bliss Bequest.  © 2003 Estate of Pablo Picasso/Artists Rights Society (ARS), New York. http://www.moma.org/ Web. (2012).

Christopher Columbus, Evolving Or Stagnant Essay

Christopher Columbus, Evolving or Stagnant? The Dogs of Paradise, which has similar characteristics as The Harp and the Shadow, is a novel that focuses on the discovery of the New World. Within his novel, Posse shines light, and hyperbolizes, Christopher Columbus as a character. Although this characterization is truly unknown to all, Posse is able to give a fictional argument of how one could portray Columbus. This paper will examine how Christopher Columbus begins as a dynamic, growing character but eventually falls into a static, and nearly childish, state. Abel Posse uses the new historical novel characteristics to demythologize Christopher Columbus. The new historical novel trend in Latin America began in the mid-to-late 1900s. Seymour Menton describes the â€Å"new historical novel† as, â€Å"†¦a combination of the comic, the documented, and the invented historical novel, these discrete categories are not very helpful in describing and analyzing the phenomenon† (Menton 16). Abel Posse uses this definition to make a grotesque, vulgar text, which concludes in making his exaggerations within the text, so real. Within new historical novels, the use of famous historical people as protagonist is a popular trend (Menton 23). Hutcheon describes these protagonist as, â€Å"†¦anything but proper types: they are ex-centrics, the marginalized, the peripheral figures of fictional history (Hutcheon 114). Posse blatantly makes Columbus out to be a non-heroic, bad man. The Dogs of Paradise beginsShow MoreRelatedOne Significant Change That Has Occurred in the World Between 1900 and 2005. Explain the Impact This Change Has Made on Our Lives and Why It Is an Important Change.163893 Words   |  656 PagesTianjin, Rangoon, Hong Kong, Singapore, and Calcutta increased at phenomenal rates, but did not come close to the absolute size of megacities such as Chicago, New York, and London. 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