AP STATISTICS LESSON THE IDEA OF PROBABILITY

ESSENTIAL QUESTION: How is probability used in Statistics? Objectives:  To develop a working understanding of Probability.  To understand what is meant by “Random,” and what it’s characteristics are in the long run.

Introduction Probability is a branch of mathematics that describes the pattern of chance outcomes. Probability is a branch of mathematics that describes the pattern of chance outcomes. The reasoning of statistical inference rests on asking, “ How often would this method give a correct answer if I used it many, many times?” The reasoning of statistical inference rests on asking, “ How often would this method give a correct answer if I used it many, many times?”

The Idea of Probability  Probability begins with the observed fact that some phenomena are random – that is, the relative frequencies of their outcomes seem to settle down to fixed values in the long run.  The big idea is this: chance behavior is unpredictable in the short run but has a regular and predictable pattern in the long run.  The tossing of a coin can not be predicted in just a few flips, but there is a regular pattern in the results, a pattern that emerges clearly only after many repetitions.

Example 6.1 Page 331 COIN TOSSING For the first few tosses the proportion of heads fluctuates quite a bit, but settles down as we make more and more tosses. For the first few tosses the proportion of heads fluctuates quite a bit, but settles down as we make more and more tosses.

Randomness and Probability Randomness in statistics is not a synonym for “haphazard” but a description of a kind of order that emerges only in the long run. Randomness in statistics is not a synonym for “haphazard” but a description of a kind of order that emerges only in the long run. The idea of probability is empirical. That is, it is based on observation rather than theorizing. The idea of probability is empirical. That is, it is based on observation rather than theorizing.

Randomness and Probability (definitions)  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.  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 relative frequency.

Thinking about Randomness  That some things are random is an observed fact about the world.  Independent – The outcome of one trial must not influence the outcome of any other.