How Odds Are Related to Probability

Many times the odds of an event occurring are posted. For example, one might say that a particular sports team is a 2:1 favorite to win the big game. What many people do not realize is that odds such as these are really just a restatement of the probability of an event. Probability compares the number of successes to the total number of attempts made. The odds in favor of an event compares the number of successes to the number of failures.  In what follows, we will see what this means in greater detail. First, we consider a little notation. Notation for Odds We express our odds as a ratio of one number to another. Typically we read ratio A:B as A to B. Each number of these ratios can be multiplied by the same number. So the odds 1:2 is equivalent to saying 5:10. Probability to Odds Probability can be carefully defined using set theory and a few axioms, but the basic idea is that probability uses a real number between zero and one to measure the likelihood of an event occurring. There are a variety of ways to think about how to compute this number. One way is to think about performing an experiment several times. We count the number of times that the experiment is successful and then divide this number by the total number of trials of the experiment. If we have A successes out of a total of N trials, then the probability of success is A/N. But if we instead consider the number of successes versus the number of failures, we are now calculating the odds in favor of an event. If there were N trials and A successes, then there were N - A B failures. So the odds in favor are A to B. We can also express this as A:B. An Example of Probability to Odds In the past five seasons, crosstown football rivals the Quakers and the Comets have played each other with the Comets winning twice and the Quakers winning three times. On the basis of these outcomes, we can calculate the probability the Quakers win and the odds in favor of their winning. There was a total of three wins out of five, so the probability of winning this year is 3/5 0.6 60%. Expressed in terms of odds, we have that there were three wins for the Quakers and two losses, so the odds in favor of them winning are 3:2. Odds to Probability The calculation can go the other way. We can start with odds for an event and then derive its probability. If we know that the odds in favor of an event are A to B, then this means that there were A successes for A B trials. This means that the probability of the event is A/(A B ). An Example of Odds to Probability A clinical trial reports that a new drug has odds of 5 to 1 in favor of curing a disease. What is the probability that this drug will cure the disease? Here we say that for every five times that the drug cures a patient, there is one time where it does not. This gives a probability of 5/6 that the drug will cure a given patient. Why Use Odds? Probability is nice, and gets the job done, so why do we have an alternate way to express it? Odds can be helpful when we want to compare how much larger one probability is relative to another. An event with a probability 75% has odds of 75 to 25. We can simplify this to 3 to 1. This means that the event is three times more likely to occur than not occur.

Stereotypical Representations Of African Culture - 1765 Words

For years now, the cinematic (Hollywood narrative films) worlds has based all sorts of their different films on Africa and its people, but are these stereotypical representations on Africa showcased in all films? Various genres such as comedy, drama, horror and even science-fiction have showcased African people showing us world cinema’s typical and ideal representation of an African character, portraying their culture poorly, negatively and violently, but not all films portray African characters negatively with no dominance. Though globally seen as poor people who live in poverty, that’s right, I said poverty, most children grow up to see Africans as just that. Poor and unfortunate. The typical African culture is generally assumed to be of poor and unfortunate civilization, undermining any positive influences that could possibly be made to Africa and its people. They are stereotyped as worthless outcasts, although films such as Tsotsi and Remember the Titans take these depictions of Africa and throughout the films, â€Å"Transform† them instantaneously in the films Tsotsi and ATL where aesthetic features such as costume, setting and mise en scene differentiate the representation of Africans to the reality in the film. Costume is one of the aesthetic features which influence the representations of Africans in the film Tsotsi. By directing certain characters in different costumes, it immediately gives the audience a solid first impression on the character and what sort of attitudesShow MoreRelatedColonialism And Racism In Crash By Paul Haggis839 Words   |  4 Pages Paul Haggis’s 2004 melodrama â€Å"Crash† is a film depicting the way diverse societies, cultures and environments affect each other’s lives. 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Chemistry Review Chapters 1 †2 Free Essays

Chemistry Review sheet: Unit 1- Lesson 1, 2 *Key notes to keep in mind* u Metals have a high low ionization energy u Non-metals have a high electron affinity  · Atom: The basic unity of an element which still retains the elements properties  · Atomic number: the unique number of protons in the nucleus of a particular element  · Isotope: Atoms of the same element which contain a different number of neutrons  · Periodic law: The chemical and physical properties of the elements repeat in a regular, periodic pattern when they are arranged according to their atomic number. Periodic trend: a pattern that is evident when elements are organized by their atomic numbers o Trends for atomic size: As you go down a group the atoms get bigger. o As you go down a group, valence electrons occupy and energy level that is farther and farther from the nucleus. We will write a custom essay sample on Chemistry Review Chapters 1 – 2 or any similar topic only for you Order Now Therefore the rings of electrons underneath the valence atoms shield the valence electrons from the nucleus so that the atom isn’t pulled in as tight as the one before it. o Trends for atomic size: As you go down a periodic table, atoms get smaller Because the protons increase as you go down a period, the positive charge on tighter to the nucleus rather looser. o Trends for ionization energy: Ionization energy tends to go down a group o As you go down a period the attraction between the nucleus and the electrons in the outer energy level decreases. o Ionization energy tends to increase across a period. o As you go across a period the attraction between the nucleus and the electrons in the outer energy level increases. Therefore, more energy is needed to pull an electron away from its atom. Lewis structure: a symbolic representation of the arrangement of the valence electrons of an element  · Octet: an arrangement of eight electrons in the valence shell of an atom  · Ioniz ation energy: the energy that is needed to remove an electron from a neutral atom  · Atomic mass unit (u): a unit of mass that is 1/12 of the mass of a carbon-12  · Radioisotope: an unstable isotope of an element, which undergoes radioactive decay  · Mass number: The total number of protons and neutrons in the nucleus of one of its atoms. Each proton or neutron is counted as one unit of the mass number. Energy level: fixed, three-dimensional volume in which electrons travel around the nucleus.  · Valence electron: an electron that occupies the outermost energy level of an atom.  · Stable octet: an arrangement of eight electrons in the valence shell of an atom.  · Electron affinity: the change in energy that accompanies the addition of an electron to an atom in the gaseous state.  · Cation: a positively charged atom.  · Anion: a negatively charged atom. Theories: Law of Conservation of mass: During a chemical reaction, the total mass of the substances involved does no t change. Law of Definite Proportions: Elements always combine to form compounds in fixed proportions by mass. (Eg. Water always contains the elements hydrogen and oxygen combined in the following proportions: 11% hydrogen, 89% oxygen) Lesson 3 Ionic and Covalent compounds  · Chemical Bonds: the forces that attract to each other in compounds. o BONDING INVOLVES THE INTERACTION BETWEEN THE VALENCE ELECTRONS OF ATOMS WHICH USUALLY CREATES A MORE STABLE BOND THAT AN ELEMENT ON ITS OWN.  · Ionic compound: between a non-metal and a metal where the metal loses an electron and the non-metal gains it Characteristics of an ionic bond consist of:  § Normally happens between a metal and a non-metal  · Metals tend to lose electrons, non-metals tend to gain them.  § Very high melting point  § Easily dissolved in water  § Good conductor of electricity, in water or on its own.  · Covalent compound: a bond between two non-metals (or a metal and a non-metal when the metal has a high electron af finity), where atoms share electrons o Characteristics of a covalent bond consist of:  § Low melting point  § When contained under high pressures or temperatures, becomes liquid  § Weak conductor of electricity Somewhat soluble o Polar covalent compound: a bond where the electronegativity is not great enough to completely bond to the other atom. Although, it does move closer to an atom, it never completely bonds. (between 0. 5 and 1. 7) This therefore means that when the electrons are partially exchanged, rather than having a + or – sign, they receive a ? + or ? – symbol  · Electronegativity: the measure of an atoms ability to attract electrons in a chemical bond. (EN) the opposite of atomic size which therefore means that as the atomic size increase, the electronegativity decreases If the electronegativity difference is 0. 00-1. 6 the bond is covalent. o If the electronegativity difference is over 1. 7 and up the bond is ionic.  · Octet rule: atoms bond in o rder to achieve an electron configuration that is the same as the electron configuration a noble gas. (8 valence electrons)  · Isoelectric: when two atoms or ions have the same electron configuration. (e. g. Cl and Ar)  · Molecular compounds: See covalent bonds  · Intramolecular forces: the forces that bond covalent bonds together  · Intermolecular forces: the forces that bond ionic bonds together Metallic bonding: in order to combine two metals both metals lose their valence electrons and combine them in a free flowing â€Å"sea† of electrons so that the electrons are shared equally by all atoms that join the bond.  · Alloy: a homogeneous mixture of two or more metals.  · Lone pairs: electron pairs that are not involved in bonding  · Bonding pairs: electron pair that are involved with bonding.  · Polar molecule: a molecule with a partial negative charge on one end and a partial positive charge on the other end.  · Non-polar molecule: a molecule that has nei ther a positive nor negative end. How to cite Chemistry Review Chapters 1 – 2, Essay examples

A Study on the Problems Faced by Teachers in a Mixed free essay sample

A Study on the Problems faced by Teachers in a Mixed-ability Class. P. Karthi, Assistant Professor, Department of English, Gobi Arts Science College, Gobichettipalayam. Mixed ability as used in ELT usually refers to the differences that exist in a group in terms of different levels of language proficiency. This might be a result of simply the amount of time they have spent for learning, their different language learning abilities or learning style preferences. Almost all groups are mixed-ability.The world of English language teaching (ELT) presents a great number of ideas and concepts, expounding a vast assortment of styles, models and techniques, but often makes a general assumption on the make-up of actual classes in which such teaching methods are to be employed. In an ideal teaching environment, we might all wish for energetic, highly-motivated and able students coupled with a limitless supply of time and resources, but the reality that many of us have to face is far from the ideal situation. For a variety of restrictive reasons there is a need for teachers to make the best use of what is available and to do so in the most productive way that ones personal teaching methodology might allow. Teaching students with mixed ability can pose a unique set of challenges. Diversity in language, culture, confidence and ability can all come into play for teachers in the classroom Working with students, sending them down different paths in order to arrive at a similar goal can be one of the most challenging things for teachers of all backgrounds.However with patience, respect and hard work all the seemingly grand problems can be overcome to the benefit of all. As such, it is our intention to present a brief, basic summary of what we believe to be a sound starting methodology for approaching classes with students of mixed abilities. As a first step in managing the diversity of student ability in the classroom, there needs to be an analysis of the needs of the students. With this analy sis the teacher will gain much ground in the effort to determine and support the needs of every student. This analysis will provide an opportunity for the students to reflect on their ability and style and prepare them for the fact that the class will not be managed in the traditional manner. While this action seems to add work for the instructor on the front end of things we think we can easily liken it to the old adage ‘an ounce of prevention is worth a pound of cure’. Upon determination of the individual student needs the teacher can strive to coordinate the students into functional learning groups based on their skills and learning pace.The construction of focus groups allows the instructor to proactively increase the effectiveness of the lesson plan and provide realistic and achievable assignments to the students. The groups can work together based on their skill level or at that time the instructor can intermingle the weaker with the advanced, which will also contribute to creating variety in the class. This method allows for all students to advance toward a mutual go al at an appropriate pace for their capacity and avoids putting them off with material that is outside of their aptitude.Provided the instructor has established focus groups based on ability or learning pace the next step is to consider the curriculum to be utilized. The instructor should prepare a collection of authentic information and materials that can be used with varying requirements for the class. These materials can be utilized in the classroom to provide different tasks for the unique skill levels so as to achieve conformity in the exercise, while utilizing realistic expectations of what can be accomplished based on individual groups.To this end the instructor can include several different versions of the same homework task in order to align with achievement levels and maximize the benefit to all the students. Ultimately in this very limited summary we feel that we need to consider the psychology of the students, the effects of this methodology on them and how to work to benefit each and every student. If caution is not taken to include all students fully the weaker students will potentially not achieve and consequently experience the natural reaction of avoiding the activities they are not successful in.Because of this reaction the ach ievement gap will only be widened rather than narrowed. To this end, instructors must make an effort to make the classes inclusive while differentiating in order to ensure student achievement across the board and not just with the better performing students. While there are so many different facets in managing a class of students with mixed abilities, by taking some basic measures teachers can manage the challenge effectively for the benefit of all. We can be certain hat we have only begun to scratch the surface of the issues faced by teachers of classes with mixed ability students, but we hope we have provided some basic building blocks for individual instructors to start with. As instructors we have the responsibility to show respect and provide reasonable attention to all students and we feel strongly that utilizing the previously stated methodology is a start down a path to achieve such ends. Differentiating Instruction for Advanced Learners in the Mixed-Ability Classroom.