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9.5 Binomial Experiments - Binomial Experiment Formula...

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3/31/2008 1 Binomial Experiments Finite Mathematics Section 9.5 Conditions for a Binomial Experiment ± The same experiment is repeated many (n) times under the same conditions. Each repetition is called a trial or a Bernoulli trial . ± Only the same two outcomes (success and failure) are possible each time the experiment is performed. ± Each time the experiment is performed, the probabilities for the two outcomes remain the same. We use p for the probability of success and q = 1 – p for the probability of failure. ± The trials are independent. The outcome of one trial has no influence on the outcome of another trial. ± We are interested in the total number of successes, not the order in which they occur. There may be 0, 1, 2, 3, …, or n successes in n trials.
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Unformatted text preview: Binomial Experiment Formula Given a binomial experiment with n independent repeated trials, p is the probability of success in a single trial, q = 1 – p is the probability of failure in a single trial, r is the number of successes . Then the probability of r successes in n trials is given by the formula: P(r successes in n trials) = ( ) r n r q p r n, C − ⋅ Probability Distribution and Expected Value for a Binomial Experiment ± The probability distribution for a binomial experiment is called a binomial probability distribution or a binomial distribution The distribution or a binomial distribution . The expected value of a binomial experiment can be found using the formula: E(X) = np ....
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