Скачать или смотреть JEE MAIN 2021 | PROBABILITY | Tricks to Solve/Most Repeated Questions with Solutions | SET 01 /Notes

Mathematics - PROBABILITY - Most expected questions for JEE Main.
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Joint Entrance Examination – Main (JEE-Main), formerly All India Engineering Entrance Examination (AIEEE), is an all India examination conducted by the National Testing Agency (NTA) for Under Graduate Engineering admissions.

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The theory of probabilities is simply the Science of logic quantitatively treated. – C.S. PEIRCE

In earlier Classes, we have studied the probability as a measure of uncertainty of events in a random experiment. We discussed the axiomatic approach formulated by Russian Mathematician, A.N. Kolmogorov (1903-1987)and treated probability as a function of outcomes of the experiment. We have also established equivalence between the axiomatic theory and the classical theory of probability
in case of equally likely outcomes. On the basis of this relationship, we obtained probabilities of events associated with discrete sample spaces. We have also studied the addition rule of probability. In this chapter, we shall discuss the important concept of conditional probability of an event given that another event has occurred, which will be helpful in understanding the Bayes' theorem, multiplication rule of probability and independence of events. We shall also learn an important concept of random variable and its probability distribution and also the mean and variance of a probability distribution. In the last section of the chapter, we shall study an important discrete probability distribution called Binomial distribution. Throughout this chapter, we shall take up the experiments having equally likely outcomes, unless stated otherwise.

Conditional Probability
Multiplication Theorem on Probability
Independent Events
Bayes' Theorem
Partition of a sample space
Theorem of total probability
Random Variables and its Probability Distributions
Probability distribution of a random variable
Mean of a random variable
Variance of a random variable
Bernoulli Trials and Binomial Distribution
Bernoulli trials
Binomial distribution
Historical Note
The earliest indication on measurement of chances in game of dice appeared in 1477 in a commentary on Dante's Divine Comedy. A treatise on gambling named liber de Ludo Alcae, by Geronimo Carden (1501-1576) was published posthumously in 1663. In this treatise, he gives the number of favourable cases for each event when two dice are thrown.