Addition And Multiplication Rules Of Probability Pdf

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4.3: The Addition and Multiplication Rules of Probability

We need a rule to guide us. What is the probability of landing on red or blue after spinning this spinner? If a single marble is chosen at random from the jar, what is the probability that it is yellow or green? In each of the three experiments above, the events are mutually exclusive. Let's look at some experiments in which the events are non-mutually exclusive.

If A and B are two independent events in a probability experiment, then the probability that both events occur simultaneously is:. In case of dependent events , the probability that both events occur simultaneously is:. You have a cowboy hat, a top hat, and an Indonesian hat called a songkok. You also have four shirts: white, black, green, and pink. If you choose one hat and one shirt at random, what is the probability that you choose the songkok and the black shirt?

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty. A simple example is the tossing of a fair unbiased coin. These concepts have been given an axiomatic mathematical formalization in probability theory , which is used widely in areas of study such as statistics , mathematics , science , finance , gambling , artificial intelligence , machine learning , computer science , game theory , and philosophy to, for example, draw inferences about the expected frequency of events. Probability theory is also used to describe the underlying mechanics and regularities of complex systems.

Statistics Dictionary

Before you order, simply sign up for a free user account and in seconds you'll be experiencing the best in CFA exam preparation. Quantitative Methods 1 Reading 8. Probability Concepts Subject 4.

What is the probability of selecting an 'vowel' first and a 'vowel' next, if the first letter is not replaced? How many license plate numbers consisting of three letters followed by three numbers are possible when repetition is allowed? Played times. Print Share Edit Delete Report an issue. Live Game Live.

The addition rule for probabilities describes two formulas, one for the probability for either of two mutually exclusive events happening and the other for the probability of two non-mutually exclusive events happening. The first formula is just the sum of the probabilities of the two events. The second formula is the sum of the probabilities of the two events minus the probability that both will occur.

The addition rule states the probability of two events is the sum of the probability that either will happen minus the probability that both will happen.

- Беккер улыбнулся и над столом протянул парню руку. Панк брезгливо ее пожал. - Проваливал бы ты, пидор. Беккер убрал руку. Парень хмыкнул.

Он оказался в узком, увешанном зеркалами туннеле, который вел на открытую террасу, уставленную столами и стульями. На террасе тоже было полно панков, но Беккеру она показалась чем-то вроде Шангри-Ла: ночное летнее небо над головой, тихие волны долетающей из зала музыки. Не обращая внимания на устремленные на него любопытные взгляды десятков пар глаз, Беккер шагнул в толпу. Он ослабил узел галстука и рухнул на стул у ближайшего свободного столика.

И больше. Женщина сочувственно кивнула. - Поссорились. На мгновение Беккер задумался.

ТРАНСТЕКСТ стонал, его корпус готов был вот-вот рухнуть.

Довольно консервативные брюки в клетку, белая блузка без рукавов. В руке красная туристская сумка фирмы Л. Белл. Светлые волосы тщательно уложены. - Прошу меня извинить, - пробормотал Беккер, застегивая пряжку на ремне.

Через каждые несколько шагов Стратмор останавливался, держа пистолет наготове, и прислушивался. Единственным звуком, достигавшим его ушей, был едва уловимый гул, шедший снизу. Сьюзан хотелось потянуть шефа назад, в безопасность его кабинета. В кромешной тьме вокруг ей виделись чьи-то лица.

Нет, но я говорю по-английски, - последовал ответ. Беккер перешел на ломаный английский: - Спасибо. Не могли бы вы мне помочь.

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When calculating probability, there are two rules to consider when determining if two events are independent or dependent and if they are mutually exclusive or not.