How do we get to know if it follows binomial distribution or not ?!.. Does every event follow it ?!.. [The image is just for reference, kindly take ANY example to explain this.]



Dear Student,


Many experiments share the common element that their outcomes can be classified into one of two events, e.g. a coin can come up heads or tails; a child can be male or female; a person can die or not die; a person can be employed or unemployed. These outcomes are often labeled as success or failure. Note : There is no connotation of goodness here. e.g., when looking at births, the statistician might label the birth of a baby girl as  success and the birth of a baby boy as  failure, but the parents wouldnt necessarily see things that way. The usual notation for Bernoulli's trial is p = probability of success, q = probability of failure = 1 - p. Note: p + q = 1. In statistical terms, A Bernoulli trial is each repetition of an experiment involving  only 2 outcomes .  A binomial distribution gives us the probabilities associated with independent, repeated Bernoulli trials. In a binomial distribution the probabilities of interest are those of receiving a certain number of successes, r, in n independent trials each having only two possible outcomes and the same probability, p, of success. So, e.g. , using a binomial distribution, we can determine the probability of getting 4 heads in 10 coin tosses. 

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When we have a bigger sample space, then it becomes quite difficult to solve such problems.Then we commonly use binomial trials.
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-When there could be only two events success or failure. -when event is independent -the probability of a event never changes
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