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Probability

Probability-Definition, Formula, Types, Problems & Solutions | Class 12 Math Notes Study Material Download Free PDF

January 17, 2025 by Neeraj Anand, Param Anand
Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability has been introduced in maths to predict how likely events are to happen.  the meaning of probability is basically the extent to which something is likely to happen. This is the basic probability theory, which is also used in the probability distribution, where you will learn the possibility of outcomes for a random experiment. To find the probability of a single event to occur, first, we should know the total number of possible outcomes.

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is …

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Conditional Probability, Solved Examples | Class 12 Math Notes Study Material Download Free PDF

January 17, 2025 by Neeraj Anand, Param Anand
Imagine a student who takes leave from school twice a week excluding sunday. If it is known that he will be absent from school on tuesday then what are the chances that he will also take a leave on saturday in the same week? It is observed that in problems where the occurrence of one event affects the happening of the following event. These cases of probability are known as conditional probability. Let us learn its definition mathematically.

Imagine a student who takes leave from school twice a week excluding Sunday. If it is known that he will …

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Multiplication Rule of Probability | Proof & Solved Examples | Class 12 Math Notes Study Material Download Free PDF

January 17, 2025 by Neeraj Anand, Param Anand
The multiplication rule of probability explains the condition between two events. For two events a and b associated with a sample space s set a∩b denotes the events in which both events a and event b have occurred. Hence, (a∩b) denotes the simultaneous occurrence of events a and b. Event a∩b can be written as ab. The probability of event ab is obtained by using the properties of conditional probability.

The multiplication rule of probability explains the condition between two events. For two events A and B associated with a …

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Independent & Mutually Exclusive Events in Probability-Definition, Venn Diagram & Solved Examples | Class 12 Math Notes Study Material Download Free PDF

January 17, 2025 by Neeraj Anand, Param Anand
Independent events are those events whose occurrence is not dependent on any other event. For example, if we flip a coin in the air and get the outcome as head, then again if we flip the coin but this time we get the outcome as tail. In both cases, the occurrence of both events is independent of each other. It is one of the types of events in probability. Let us learn here the complete definition of independent events along with its venn diagram, examples and how it is different from mutually exclusive events.

Independent events are those events whose occurrence is not dependent on any other event. For example, if we flip a …

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Bayes Theorem | Definition, Proof, Formula, Derivation & Solved Examples | Class 12 Math Notes Study Material Download Free PDF

January 17, 2025 by Neeraj Anand, Param Anand
Bayes’ theorem describes the probability of occurrence of an event related to any condition. It is also considered for the case of conditional probability. Bayes theorem is also known as the formula for the probability of “causes”. For example: if we have to calculate the probability of taking a blue ball from the second bag out of three different bags of balls, where each bag contains three different colour balls viz. Red, blue, black. In this case, the probability of occurrence of an event is calculated depending on other conditions is known as conditional probability.  in this article, let us discuss the statement and proof for bayes theorem, its derivation, formula, and many solved examples.

Bayes’ theorem describes the probability of occurrence of an event related to any condition. It is also considered for the …

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Probability Distribution | Definition, Types, Formula, Examples | Class 12 Math Notes Study Material Download Free PDF

January 17, 2025 by Neeraj Anand, Param Anand
In statistics, the probability distribution gives the possibility of each outcome of a random experiment or event. It provides the probabilities of different possible occurrences.

In Statistics, the probability distribution gives the possibility of each outcome of a random experiment or event. It provides the …

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Probability Bernoulli Trial & Binomial Distribution of Random Variables | Class 12 Math Notes Study Material Download Free PDF

January 17, 2025 by Neeraj Anand, Param Anand
Bernoulli trials and binomial distribution are explained here in a brief manner.   bernoulli’s trial is also said to be a binomial trial. In the case of the bernoulli trial, there are only two possible outcomes. But, in the case of the binomial distribution, we get the number of successes in a sequence of independent experiments.

Bernoulli Trials and Binomial Distribution are explained here in a brief manner.  Bernoulli’s trial is also said to be a …

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