SWBAT: -Calculate probabilities using the geometric distribution -Calculate probabilities using the Poisson distribution Agenda: -Review homework -Notes:

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SWBAT: -Calculate probabilities using the geometric distribution -Calculate probabilities using the Poisson distribution Agenda: -Review homework -Notes: Geometric and Poisson distributions -Homework

Binomial Probability - the probability of exactly x success in n trials P(x) = n C x p x q n-x Using the calculator to find Binomial Probabilities Binomial Probability - binompdf(n, p, x) finds probability of exactly x 2 nd VARS A - binompdf(n, p,{ x}) finds probability of more than one x 2 nd VARS B Review

Geometric Distribution - calculates the probability an experiment will take x attempts to achieve its first success P(x) = pq x-1 p = probability of success q = 1 – p = probability of failure x = number of attempts until first success Experiment must meet 4 conditions: 1. trial is repeated until first success 2. trials are independent of each other 3. probability of success, p, must remain the same for each trial 4. variable x is the number of attempts until first success

The probability of passing the bar exam the first time is 71%. What is the probability of passing it on the 4 th try? P(4) = (.71)(.29) 3 What is the probability of passing it on the 2 nd or 3 rd try? P( 2 or 3) = P(2) + P(3) = (.71)(.29) + (.71)(.29) 2 = =.266 =.017 Using the calculator geometpdf(p,x) – probability of success on the x th attempt 2 nd Vars E

Poisson Distribution - Calculates the number of success that will occur during a given time interval P(x) = µ = average number of occurrences e x = exponential function x = number of occurrences Must satisfy the following conditions: 1. probability of occurring is the same for each interval 2. occurrences in each interval are independent of occurrences in other intervals 3. count the number of occurrences, x, during a given interval

Using the calculator poissonpdf(µ, x) calculates the probability that event will occur x times during the interval poissoncdf(µ, x) calculates the probability that event will occur x or fewer times during the interval 1 - poissoncdf(µ, x) calculates probability that event will occur more than x times during the interval

=.090

Homework Pg 222 # 2 – 24 even