Solved Problems On Bayes Theorem

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Union of Events – The union of two or more events is basically the combined set of the two or more events in the sample space.

For example, the union of getting a king or hearts in a deck of cards would include 16 cards (13 hearts and 3 kings).

Bayesian inference is an important technique in statistics, and especially in mathematical statistics.

Bayesian updating is particularly important in the dynamic analysis of a sequence of data. Suppose it is late evening and you want to know if the light bulb in a room is switched on or switched off.

Bayes’ Theorem is a basic but very useful concept in data analytics.

It can be used in many problems to that deal with probability.Let us understand this theorem with the help of a simple example. There are two shapes of chocolate – round and flat. We would like to find out the probability of getting a round chocolate given that the we have already got a round chocolate out.This can be solved by using the Bayes’ theorem in the following way: P(1) = Probability of getting a round chocolate at the first pick = 7/15 P(2) = Probability of getting a round chocolate at second pick = 6/14 P(1 and 2) = ½*(6/14) P(2/1) = P(1 and 2)/P(1) = 0.214/0.4667=0.4585So the probability of getting a round chocolate on the second picking given that the first picking yielded a round chocolate is 45.85%.Bayesian inference is an extremely powerful set of tools for modeling any random variable, such as the value of a regression parameter, a demographic statistic, a business KPI, or the part of speech of a word.We provide our understanding of a problem and some data, and in return get a quantitative measure of how certain we are of a particular fact.Aman loves to write motivational articles to help students perform well in JEE and to understand the principles of Data Science.What will happen if you grab a solid rock and throw it at your neighbor’s window?The most common result is that the window will break.If your neighbor later asks if you know anything about the incident, you can confidently inform him that his window was broken you threw a rock at it earlier. But what if it wasn’t you who broke the window and, in fact, you have no idea what broke it? Was there a large temperature difference between the center and the periphery of the glass which caused a spontaneous breakage?Event – An event is simply the outcome of an experiment.For example, if you pick out a card and get a queen of spades, it is an event.

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