Here you will learn what is the probability of an event formula with examples. Let’s begin – Probability of an Event Definition : If there are n elementary events associated with a random experiment and m of them are favourable to an event A, then the probability of happening or occurrence of A is denoted […]
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Here you will learn law of total probability theorem with examples. Let’s begin – Total Probability Theorem (Law of Total Probability) Let an event A of an experiment occurs with its n mutually exclusive and exhaustive events \(B_1,B_2,B_3….B_n\) then total probability of occurrence of event A is P(A) = \(P(AB_1)\) + \(P(AB_2)\) +……..+ \(P(AB_n)\) P(A)
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Here you will learn formula for multiplication theorem probability with examples. Let’s begin – Multiplication Theorem Probability It is called compound probability or multiplication theorem. It says the probability that both A and B occur is equal to the probability that A occur times the probability that B occurs given that A has occurred. If
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Here you will learn some probability examples for better understanding of probability concepts. Example 1 : From a group of 10 persons consisting of 5 lawyers, 3 doctors and 2 engineers,four persons are selected at random. The probability that selection contains one of each category is- Solution : n(S) = \(^{10}C_4\) = 210 n(E)= \(^5C_2
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Here you will learn addition theorem of probability for two and three events with statement and proof. Let’s begin – Addition Theorem of Probability For two events : If A and B are two events associated with a random experiment, then P(\(A \cup B\)) = P(A) + P(B) – P(\(A \cap B\)) Proof : Let S
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Here, you will learn the definition of bayes theorem and the formula for bayes theorem with example. Let’s begin – Formula for Bayes Theorem Let an event A of an experiment occurs with its n mutually exclusive & exhaustive events \(B_1\), , \(B_2\), \(B_3\),………\(B_n\) & the probabilities P(A/\(B_1\)), P(A/\(B_2\))……..P(A/\(B_n\)) are known, then P(\(B_i\)/A) = \(P(B_i).P(A/B_i)\over
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Here, you will learn formula for binomial probability distribution in probability with example. Let’s begin – Suppose that we have an experiment such as tossing a coin or die repeatedly or choosing a marble from an urn repeatedly. Each toss or selection is called a trial. In any single trial there will be a probability
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Here, you will learn dependent and independent events in probability with examples. Let’s begin – Dependent and Independent Events Formula Two Events A and B are said to be independent if occurrence or non-occurrence of one does not affect the probability of the occurrence or non-occurrence of other. If the occurrence of one event affects
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Here, you will learn formula for conditional probability and properties of conditional probability with examples. Let’s begin – Formula for Conditional Probability Let A and B be two events associated with a random experiment. Then, the probability of occurrence of event A under the condition that B has already occured and P(B) \(\ne\) 0, is
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Here, you will learn probability basic concepts and definitions of probability. Let’s begin – Probability gives us a measure of likelihood that something will happen. However probability can never predict the number of times that an occurrence actually happens. Probability Basic Concepts and Definitions (a) Experiment : An action or operation resulting in two or
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