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ANATOMY OF BINOMIAL PROBABILITIES

ANATOMY OF BINOMIAL PROBABILITIES. A Binomial Distribution is a form of a discrete probability distribution having only two outcomes. A Binomial Probability is the result of an experiment conducted on a Binomial Distribution. These distributions have the following four characteristics:

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ANATOMY OF BINOMIAL PROBABILITIES

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  1. ANATOMY OF BINOMIAL PROBABILITIES • A Binomial Distribution is a form of a discrete probability distribution having only two outcomes. A Binomial Probability is the result of an experiment conducted on a Binomial Distribution. These distributions have the following four characteristics: • There are only two outcomes for each trial. • The experiment must have a fixed number of trials. • The trials must be independent. • The probabilities for success and failure must remain constant for all trials. The Formula: Often the formula appears as written below, where the combination representing the number of success, x, in n trials, nCx , is replaced by . Number of successes (x) Number of failures (n-x) The number of ways to obtain x successes in n trials = = Probability of success (p) Probability of failure (q) EXAMPLE: Knowing that 10% of the population is left-handed, what is the probability that a class of 10 students will have exactly 2 left-handed members? Given: n = 10 x = 2 p = .1 q = .9 Does this problem meet the criteria for a binomial probability? Yes.

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