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Understanding Binomial Probabilities with Fixed Number of Trials

Learn about binomial experiments with fixed number of trials, independent outcomes, and probabilities of success. Calculate probabilities of successes in multiple trials with examples included.

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Understanding Binomial Probabilities with Fixed Number of Trials

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  1. Chapter 5 Section 2: Binomial Probabilities

  2. trial – each time the basic experiment is performed

  3. Properties of a Binomial Experiment • fixed number of trials, denoted n • each trial is independent and identical • each trial has two possible outcomes - one outcome is success (S) P(S) = p - one outcome is failure (F) P(F) = q - the values of p and q do not change from one trial to another • find the probability of r successes out of n trials

  4. Formula P(r) =

  5. Example You have three multiple choice questions to answer, each with four choices. What is the probability you get zero, one, two, or all three questions correct?

  6. Example Assume that when a certain hunter shoots at a pheasant, the probability of hitting it is 0.6. Find the probability that the hunter a. will hit exactly four of the next five pheasants at which he shoots b. will hit at least four of the next five c. will hit at least one of the next five

  7. Example Thirty percent of the voters in a large voting district are veterans. If 10 voters are randomly selected, find the probability that less than five will be veterans.

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