Addition Rules in Probability and Statistics

Addition rules are important in probability. These rules provide us with a way to calculate the probability of the event A or B, provided that we know the probability of A and the probability of B. Sometimes the or is replaced by U, the symbol from set theory that denotes the union of two sets. The precise addition rule to use is dependent upon whether event A and event B are mutually exclusive or not. Addition Rule for Mutually Exclusive Events If events A and B are mutually exclusive, then the probability of A or B is the sum of the probability of A and the probability of B.   We write this compactly as follows: P(A or B) P(A) P(B) Generalized Addition Rule for Any Two Events The above formula can be generalized for situations where events may not necessarily be mutually exclusive. For any two events A and B, the probability of A or B is the sum of the probability of A and the probability of B minus the shared probability of both A and B: P(A or B) P(A) P(B) - P(A and B) Sometimes the word and is replaced by ∠©, which is the symbol from set theory that denotes the intersection of two sets. The addition rule for mutually exclusive events is really a special case of the generalized rule. This is because if A and B are mutually exclusive, then the probability of both A and B is zero. Example #1 We will see examples of how to use these addition rules. Suppose that we draw a card from a well-shuffled standard deck of cards. We want to determine the probability that the card drawn is a two or a face card. The event a face card is drawn is mutually exclusive with the event a two is drawn, so we will simply need to add the probabilities of these two events together. There are a total of 12 face cards, and so the probability of drawing a face card is 12/52. There are four twos in the deck, and so the probability of drawing a two is 4/52. This means that the probability of drawing a two or a face card is 12/52 4/52 16/52. Example #2 Now suppose that we draw a card from a well-shuffled standard deck of cards. Now we want to determine the probability of drawing a red card or an ace. In this case, the two events are not mutually exclusive. The ace of hearts and the ace of diamonds are elements of the set of red cards and the set of aces. We consider three probabilities and then combine them using the generalized addition rule: The probability of drawing a red card is 26/52The probability of drawing an ace is 4/52The probability of drawing a red card and an ace is 2/52 This means that the probability of drawing a red card or an ace is 26/524/52 - 2/52 28/52.

Benefits Of Forming A Corporation - 1101 Words

Corporation Student Name: Kerri Robinson Institution: Fitchburg State University One of the four types of firms is a corporation. A corporation is a legally defined, artificial being, separate from its owners. Corporations have as many legal powers that people have. For example corporations can enter contracts, acquire assets, and incur obligations. (Berk DeMarzo, 2014) Choosing the right business structure is very important. Different businesses offer different types of protection against legal action than others. This is why corporations often are popular. A corporation is viewed as its own entity and rarely can someone sue a corporation and go after personal assets of board members. Consider the following advantages†¦show more content†¦(Wolfe, 2016) After reading those great advantages to forming a corporation you should keep in mind that there are disadvantages as well. This section of the paper will review some of the big disadvantages to a corporation. Corporations can be an expensive start up. Often times there are many filing fees. On top of the filing fees, if your corporation is a nonprofit there are even more fees and paperwork to do. Depending on the state you’re in there may be more filling that needs to get done. This may not be a big deal to all but if you are limited on cash to start these fees will add up even if their small. Next corporations have many rules to follow. Corporations must follow certain standards by the law on how they govern themselves. For instance, it is required for a corporation to have a board of directors, hold meetings at determined intervals, and keep certain records. When a corporation sells stock or if they have a members other rules will apply as well. If your business is your idea and passion then you should consider the type of structure to form it as you don’t want to get left out. It is important to understand that one person cannot personally own the corporation. The board o f directors is dictated by federal and state rules. For instance oftentimes family members and spouses cannot serve on a small corporations board at the same time. Another important thing to understand is that even if you start aShow MoreRelatedAdvantages and Disadvantages of Forming a Business811 Words   |  4 Pages1. List down the advantages and disadvantages of forming a partnership * Collaboration. As compared to a sole proprietorship, which is essentially the same business form but with only one owner, a partnership offers the advantage of allowing the owners to draw on the resources and expertise of the co-partners. Running a business on your own, while simpler, can also be a constant struggle. 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Procedure Skills Free Essays

Lesson planSchool: Colegiul Na?ional M. Eminescu, Ia?i Date: 6th April 2018 Proposer: Popovics Anamaria Mentor’s name: Cetilina Neagu Class: 9th grade, 5 classes/ week Level: B2 Textbook: Upstream Intermediate Lesson type: Integrated skills with focus on consolidating and acquiering vocabulary related to sports and sportspeople Time allowed: 50 minutes Aids: Textbook, blackboard, chalk Aims: Create the opportunity for Ss to use previously acquired language related to sports. Give Ss the opportunity to express their own opinions on different types of sports. We will write a custom essay sample on Procedure Skills or any similar topic only for you Order Now Objectives: By the end of the lesson Ss will have retold the text using vocabulary related to sports. Ss will have learnt how to use arguments for their own opinions. Ss will have acquired new vocabulary (adjectives) related to sports. Time and lesson stage Procedure Skills Interaction Rationale and observations2 minutesWarm-up T will ask how was their previous day after school, and also ask them to remember the last text they did Speaking T-Ss To create a relaxing environment and also revise language.10 minutes Controlled speaking practice T: Will ask ss. provide the main ideas from and remember the important words.Speaking T-Ss Teacher can provide key words to trigger the idea and guide them towards what she needs to hear from the students using the appropriate vocabulary.20 minutes Free speaking practice8 minutes Controlled Practice T tasks Ss to describe pictures related to sports and make connections between these and the type of people who would practice the sports.T asks the Ss to solve ex 2 from page 136. The T will explain words along the way and demand synonyms for groups of words and words such as â€Å"centre of the target†, â€Å"daring†. Writing + Speaking +FeedbackPairsStudents will have developed conversational skills through dialogueProvide arguments.Describe by using appropriate adjectives.Paragraph organising.8minutes T puts the students into pairs and asks them to solve exercise 4 from the page 137. The teacher will then place three stickers on the blackboard depicting the words â€Å"interesting†, â€Å"challenging† and â€Å"boring† and ask the students to complete the gaps underneath them with the free-time activities they came up with earlier. Speaking/ PairworkGroupwork Pairs -Agreeing, disagreeing, giving arguments, interrupting, summing up, reporting to the classPeer feedback2 minutes T gives feedback upon the activities and gives homework to the ss : The students will have to revise the conditionals from the end of their practice books and come up with sentences of each conditional type. Speaking T-Ss To revise the previous activities. How to cite Procedure Skills, Papers

Finding Yourself free essay sample

Here is a world which beautiful and terrible things happen. A world which has life on it. So what is life? Life is the existence as a human being. It is being alive, the ability to function and grow. Grow in the sense that it is to experience misery, loneliness, suffering, happiness and all other feelings you’ve thought you will never experience. In other words, life is full of many unpredictable things. â€Å"What is the meaning my life?† I remember the time when I asked myself the same question before. At that time, I was alone and thinking also who and what am I after all? Who am I after many years from now? And who am I before dying? Condone me for uttering death because we really can’t deny that there will be and there will always be death after life. I wonder why great people go into their graves with their greatness still in them. We will write a custom essay sample on Finding Yourself or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page They are not just great because they are famous or what. It’s because they died great because they found their selves. They fulfilled their desires or ambitions. They showed their greatness to people who idolizes them. They proved their selves. That made me realize that life is worthless if you haven’t fulfilled what you want. I also believe in what Mahatma Gandhi, he said that â€Å"where there is love, there is life.† Yah that’s true. The word love is a too broad term. Some say that if you are in loved. Things are brighter, things seems clearer and there is a euphoric feeling of contentment. Think about how you feel when you are in love. You feel unexplainable joy in yourself. To know that someone adores you or loves you unconditionally, seems to make everything alright. You feel like you have everything you wanted to. You feel the contentment and satisfaction†¦ and that’s what life should feel like. Life is so meaningful with the presence of love. I think that now, I must begin to look, look for the things I can do that will put me to some commitment in life. That will enable me to do some things that uses my capabilities that I have and also to feel my contentment, satisfaction and especially happiness. We are what we think we are. We are as old as we feel, as rich as our imagination, as strong as our faith, and as weak as our fears. It is these things that make up life for us. It is our mind, it is us, it is our choices that makes the world and our minds are exactly what we make them. The only thing is that there is no one answer or exact answer to what life’s meaning, because its different for everyone. The meaning of life is to achieve whatever it is we set ourselves to do in our short time on this world.There will always be those who search and search for straight answers but most likely answers they will never find. Whatever your passion, whatever your desire or ambition, fulfill it with your greatest potential and you will find the meaning of your life.