Section The Idea of Probability Statistics

Probability is studied… When looking at games of chance ◦ cards, dice, lotteries When looking at social science data ◦ Life, death When looking at scientific data ◦ Variations in individual measurement are random AP Statistics, Section 6.1, Part 12

The idea of probability To understand why we can trust random samples and randomized comparative experiments, we must look closely at chance behavior. AP Statistics, Section 6.1, Part 13

Random is not “haphazard” The Big Idea: “Chance behavior is unpredictable in the short run but has a regular and predictable pattern in the long run.” AP Statistics, Section 6.1, Part 14

Definition of Random We call a phenomenon random if individual outcomes are uncertain but there is nonetheless a regular distribution of outcomes in a large number of repetitions. AP Statistics, Section 6.1, Part 15

Definition of Probability The probability of any outcome of a random phenomenon is the proportion of times the outcome would occur in a very long series of repetitions. That is, probability is long-term frequency. Computer simulations can allows us to see those long-term frequencies AP Statistics, Section 6.1, Part 16

Independence In order for an event to be considered random, it must be independent. That is, it must not be influenced by other (perhaps previous) events. Example: ◦ Flipping a head does not make it more probable that a tail will occur next. AP Statistics, Section 6.1, Part 17

Simulations Cory rolls a die 30 times. How often does a number of 2 or less appear? AP Statistics, Section 6.1, Part 18

Create the random numbers AP Statistics, Section 6.1, Part 19

Categorize the results AP Statistics, Section 6.1, Part 110

Count the results AP Statistics, Section 6.1, Part 111

Consider During the last simulation, Cory “rolled” numbers two or less 11 times. (36.7%) Is this what you expected? Why wasn’t it exactly 10. What would happen if Cory “rolled” 300 times? AP Statistics, Section 6.1, Part 112

300 Trials With 300 “rolls”, Emil got a number less than two, 90 times (30%). What was expected? AP Statistics, Section 6.1, Part 113

Simulating tossing multiple coins AP Statistics, Section 6.1, Part 114

What about things you can’t “simulate” Spin a penny on your desk. ◦ How many times does it fall heads up? ◦ What is the probability that it fall heads up? Toss a thumbtack on a hard surface 100 times. ◦ How times did it lands point up? ◦ What is the probability that it lands point up? AP Statistics, Section 6.1, Part 115

Assignment Exercises: AP Statistics, Section 6.1, Part 116