1. 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 8.2.2 1

2. Section 8.2 Geometric Distributions AP Statistics

3. AP Statistics, Section 8.2.2 3 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

4. AP Statistics, Section 8.2.2 4 Formulas for Geometric Distribution These formulas are not AP Testable. How many rolls would you expect before I have a success? Find the mean.

5. AP Statistics, Section 8.2.2 5 Formulas for Geometric Distribution These formulas are not AP Testable.

6. AP Statistics, Section 8.2.2 6 2 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

7. AP Statistics, Section 8.2.2 7 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)

8. AP Statistics, Section 8.2.2 8 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

9. AP Statistics, Section 8.2.2 9 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)

10. AP Statistics, Section 8.2.2 10 Better formulas

11. AP Statistics, Section 8.2.2 11 Exercises 8.37-8.40, 8.41-8.53 odd (Due Wed) Chp 8 Review 8.55-8.65 odd (Due Thurs)