Warm Up Describe a Binomial setting. Describe a Geometric setting. When rolling an unloaded die 10 times, the number of times you roll a 6 is the count X off successes in each independent observations. 1. Is this a Binomial or Geometric Distribution? 2. How would you describe this with “B” notation? 3. I want to know the probability of getting at most 2 of the 10 rolls will be a success. Describe and calculate the binomial probability. AP Statistics, Section

Section 8.2 Geometric Distributions AP Statistics

AP Statistics, Section The Geometric Setting 1. Each observation falls into one of just two categories, which for convenience we call “success” or “failure” 2. You keep trying until you get a success 3. The observations are all independent. 4. The probability of success, call it p, is the same for each observation. X is the number of trials it takes to get a success(including the success). At least one up to infinity. This is an Infinite distribution Make sure you can define X for both types Bi- # of successes Geo- # until a success

AP Statistics, Section Formulas for Geometric Distribution These formulas are not AP Testable. How many rolls would you expect before I have a success? Find the mean.

AP Statistics, Section Formulas for Geometric Distribution These formulas are not AP Testable.

AP Statistics, Section nd roll probability is the probability of a failure followed by a success. 1 fail before success 5/6*1/6 2 fail before success 5/6*5/6*1/6 3 fail before success 5/6*5/6*5/6* 1/6

AP Statistics, Section Calculating Probabilities The probability of rolling a 6=1/6 EX: The probability of rolling the first 6 on the first roll:  P(X=1)=1/6.  geometpdf(1/6,1) Go to 2 nd  VARS  E EX: The probability of rolling the first 6 after the first roll:  P(X>1)=1-1/6.  1-geometcdf(1/6,1)

AP Statistics, Section Calculating Probabilities The probability of rolling a 6=1/6 Ex: The probability of rolling the first 6 on the second roll:  P(X=2)=(1/6)*(5/6).  geometpdf(1/6,2) Ex: The probability of rolling the first 6 on the second roll or before:  P(X<2)=(1/6) +(1/6)*(5/6)  geometcdf(1/6,2) That point or below

AP Statistics, Section Calculating Probabilities The probability of rolling a 6=1/6 Ex: The probability of rolling the first 6 on the second roll:  P(X=2)=(1/6)*(5/6).  geometpdf(1/6,2) Ex: The probability of rolling the first 6 after the second roll:  P(X>2)=1-((1/6) +(5/6)*(1/6))  1-geometcdf(1/6,2)

AP Statistics, Section Better formulas

AP Statistics, Section Exercises , odd (Due Wed) Chp 8 Review odd (Due Thurs)