AP STATISTICS LESSON AP STATISTICS LESSON PROBABILITY MODELS

ESSENTIAL QUESTION: What is a probability model and how can it be used to solve statistics problems? Objectives:  To define and use the vocabulary of probability.  To design probability models that fit real–life problems.

Basic Descriptions of Probability Models  A list of all possible outcomes.  A probability for each outcome. For example, the probability model for a coin toss is one out of two possible outcomes (i.e., heads or tails). The description of coin tossing has two parts:

Probability Models  The sample space S of a random phenomenon is the set of all possible outcomes. ( Each member of S is a possible sample, which explains the term sample space.)  An event is any outcome or a set of outcomes of a random phenomenon. That is, an event is a subset of the sample space.  A probability model is a mathematical description of a random phenomenon consisting of two parts: a sample space S and a way of assigning probabilities to events.  The sample space S can be very simple or very complex.

Example 6.3  2 dice page 336.  Probability of rolling a five.  To specify S, we must state what constitutes an individual outcome and then state which outcomes can occur.

Example 6.4  Let your pencil point fall blindly into Table B of random digits: record the value of the digit it lands on. The possible outcomes are S = ( 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 ) S = ( 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 )

Example 6.5  An experiment consists of flipping a coin and rolling a die. Find the sample space. Use a tree diagram to represent the possible outcomes.

Multiplication Principle If you can do one task in a number of ways and a second task in b number of ways, then both tasks can be done in a x b number of ways.

Example 6.6  Flipping four coins. What is the size of the sample space and find all possibilities. Use number of heads to organize. The possible outcomes of an SRS of 1500 people are the same as when flipping a coin 1500 times when a question is answered “yes” or “no”.

Generating a random decimal number  Example 6.7 Page 339  Limitation is the capability of the calculator or computer.

Additional Definitions With replacement refers to the drawing of an object, recording the selection and then putting it back so that it may be drawn again. Without replacement refers to the drawing of an object, recording the selection and then not putting it back so it can’t be drawn again.