# bayes' theorem in probability

For a detailed discussion on the concept of Bayes’ theorem, download BYJU’S – The Learning App. Using the Bayes’ theorem, we can find the required probability: Thus, the probability that the shares of a company that replaces its CEO will grow by more than 5% is 6.67%. Bayes theorem is also known as the formula for the probability of “causes”. Although the high-low method is easy to apply, it is seldom used, as it can distort costs due to its reliance on two extreme values from a given data set. Basically, it is a decision-making tool that helps businesses cope with the impact of the future’s uncertainty by examining historical data and trends. The CEO is responsible for the overall success of an organization and for making top-level managerial decisions. Bayes theorem is also known as the formula for the probability of “causes”. \(P(E_i ∩ A)~= ~P(E_i)P(A │E_i)\)⋯⋯⋯⋯⋯⋯⋯⋯(2), Using total probability theorem, From the remaining cards of a pack, two cards are drawn and both are found to be the diamond cards. In statistics and probability theory, the Bayes’ theorem (also known as the Bayes’ rule) is a mathematical formula used to determine the conditional probability of events. Bayes’ Theorem governs the likelihood that one event is based on the occurrence of some other events. Some illustrations will improve the understanding of the concept. CFI offers the Financial Modeling & Valuation Analyst (FMVA)™FMVA® CertificationJoin 350,600+ students who work for companies like Amazon, J.P. Morgan, and Ferrari certification program for those looking to take their careers to the next level. From the pack of 52 cards, one card is lost. Bayes’ theorem describes the probability of occurrence of an event related to any condition. Generally, in Supervised Machine Learning, when we want to train a model the main building blocks are a set of data points that contain features (the attributes that define such data points),the labels of such data point (the numeric or categorical tag which we … P(A) – the probability of event A 4. Let \(A\) be the event that the man reports that number four is obtained. At the end of the year, one student is chosen at random and found that he/she has an A grade. Find the probability that the number obtained is actually a four. One ball is drawn at random from one of the bags, and it is found to be black. Moreover, statistics concepts can help investors monitor, In statistics and probability theory, independent events are two events wherein the occurrence of one event does not affect the occurrence of another event, – the probability of event B occurring given that event A. According to the conditional probability formula, \(P(E_i│A)~=~\frac{P(E_i ∩ A)}{P(A)}\) ⋯⋯⋯⋯⋯⋯⋯⋯(1), Using the multiplication rule of probability, Then, \(P(E_1)\) = Probability that four occurs = \(\frac{1}{6}\), \(P(E_2)\) = Probability that four does not occurs = \(1 ~–~ P(E_1) ~=~ 1~-\frac{1}{6}~ =~\frac{5}{6}\), Also, \(P(A|E_1)\) = Probability that man reports four and it is actually a four = \(\frac{2}{3}\), \(P(A|E_2)\) = Probability that man reports four and it is not a four = \(\frac{1}{3}\). In Probability, Bayes theorem is a mathematical formula, which is used to determine the conditional probability of the given event. Imagine you are a financial analyst at an investment bank. In this article, let us discuss the statement and proof for Bayes theorem, its derivation, formula, and many solved examples. The theorem is named after English statistician, Thomas Bayes, who discovered the formula in 1763. Previous year result reports that 30% of all students who stay in the hostel scored A Grade and 20% of day scholars scored A grade. Then,\(P(E_1)~ = ~P(E_2)~ =~\frac{1}{2}\), Also,\(P(A|E_1) ~= ~P\)(drawing a black ball from Bag I) = \(\frac{6}{10}~ = ~\frac{3}{5}\), \(P(A|E_2) ~=~ P\)(drawing a black ball from Bag II) = \(\frac{3}{7}\). Bayes' theorem From law of total probability By using Bayes’ theorem, probability that number obtained is actually a four, \(P(E_1 |A)~ \) \(= \large \frac{P(E_1)P(A|E_1)}{P(E_1 )P(A│E_1 )~+~ P(E_2)P(A|E_2)}~ The formula for Bayes theorem is: A bag I contain 4 white and 6 black balls while another Bag II contains 4 white and 3 black balls. As mentioned in the previous post, Bayes’ theorem tells use how to gradually update our knowledge on something as we get more evidence or that about that something. \(P(A)~=~\sum\limits_{k=1}^{n}~P(E_k)P(A| E_k)\)⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯(3), Putting the values from equations (2) and (3) in equation 1, we get, \(P(E_i│A)~=~\frac{P(E_i)P(A│E_i)}{\sum\limits_{k=1}^n~P(E_k)P(A| E_k)}\). A mathematical formula used to determine the conditional probability of events, The Total Probability Rule (also known as the law of total probability) is a fundamental rule in statistics relating to conditional and marginal, A solid understanding of statistics is crucially important in helping us better understand finance. Of the students in the college, 60% of the students reside in the hostel and 40% of the students are day scholars. Read a job description, Join 350,600+ students who work for companies like Amazon, J.P. Morgan, and Ferrari. The CEO is responsible for the overall success of an organization and for making top-level managerial decisions. He throws a die and reports that the number obtained is a four. As we know, Bayes theorem defines the probability of an event based on the prior knowledge of the conditions related to the event. P(B|A) – the probability of the CEO replacement given the stock price has increased by 5%. Also the numerical results obtained are discussed in order to understand the possible applications of the theorem. Bayes Theorem is a mathematic model, based in statistics and probability, that aims to calculate the probability of one scenario based on its relationship with another scenario. It is also considered for the case of conditional probability. A ball is drawn at random, its color is noted, and again the ball is returned to the bag. \(P(A)~=~\sum\limits_{k=1}^{n}~P(E_k)P(A| E_k)\), ) is considered as the priori probability of hypothesis E, |A) is considered as the posteriori probability of hypothesis E, Bayes Theorem can be derived for events and. Bayes theorem is also known as the formula for the probability of “causes”. In such a case, the theorem is expressed in the following way: In the special case above, events A– and A+ are mutually exclusive outcomes of event A. Bayes' theorem to find conditional porbabilities is explained and used to solve examples including detailed explanations. Your email address will not be published. Moreover, statistics concepts can help investors monitor, the Bayes’ theorem is also used in various disciplines, with medicine and pharmacology as the most notable examples.

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