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14111cn8.9-11

# 14111cn8.9-11 - c Kendra Kilmer Section 8.4 The Binomial...

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c Kendra Kilmer October 27, 2011 Section 8.4 - The Binomial Distribution Binomial Experiments have the following properties : 1. The number of trials in the experiment is fixed. 2. There are 2 possible outcomes in each trial: “success” and “failure” 3. The probability of success in each trial is the same. 4. Trials are independent of each other. Calculating a Binomial Probability : 1. Determine if the experiment is binomial. 2. Determine the number of trials (n). 3. Define “success” in the experiment and determine the probability of that success occuring (p). 4. Determine the number of “successes” desired (r). 5. Calculate the desired probability: (a) By hand, the probability is found by doing the following calculation: P ( X = r ) = C ( n , r ) p r ( 1 - p ) ( n - r ) (b) We can use the calculator functions binompdf( or binomcdf( to do these calculations for us. Example 1 : What is the probability of exactly 3 successes in 6 trials of a binomial experiment in which p = 1 / 2?

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