Name _________________________
AP Stats
6 Probability and Simulation: The Study of Randomness
6.2 Probability Models
Objectives
 Explain what is meant by a probability model.
 Construct a tree diagram.
Date _______
 Use the multiplication principle to determine the number of outcomes in a sample
space.
 Explain what is meant by sampling with and without replacement.
Probability Models
We need a mathematical description, or model for randomness. The vocabulary for all
_______________ __________ is as follows:
The __________ _________ ___ of a random phenomenon is the set of all possible outcomes. (whether discrete or continuous)
An ________ is any outcome or set of outcomes of a random phenomenon. Therefore an event is a _________ of the sample space.
A probability model is a mathematical description of a __________ phenomenon consisting of two parts: a sample space and a way of assigning probabilities to events.
To specify S, we must state what constitutes an ______________ outcome and then state which outcomes can __________. Each member of S is a possible _________, which explains the term sample _________.

Being able to number the outcomes in a sample space is obviously critical in determining
_____________.
Three techniques to make sure no outcomes are overlooked:
1.
Tree diagrams
2.
Multiplication Principle
3.
Organized list of possible outcomes
TREE DIAGRAM
Construct a tree diagram for tossing a coin and then rolling a die.
MULTIPLICATION PRINCIPLE
If you can do one task in n
1
number of ways and a second task in n
2
number of ways, then both tasks can be done in ____________ number of ways.
How many possible outcomes are in the sample space of spinning this spinner and rolling this die?

ORGANIZED LIST
How can we make an organized list of the sample space for flipping a coin 4 times in succession?
1 Head 2 Heads 3 Heads 4 Heads 0 Heads
In mathematics, essential features of quite different phenomena can be described by the same mathematical __________. Ex. The possible outcomes of an SRS of 1500 people in a yes/no opinion poll are the same in principle as the possible outcomes of tossing a coin 1500 times.
Unfortunately some sample spaces are too large to list.
We have seen how our calculators can generate a random number for a discrete set of numbers. Our calculators can also generate a number from a continuous sample space such as between 0 and 1.
S = {all numbers between 0 and 1}
Sampling with replacement-if you want the second “draw” to have the same probability of any particular event occurring then you use replacement.
Sampling without replacement-if you don’t replace whatever was selected the first time then the probability of future events have changed due to whatever was picked the first time.
Example- How many license plates can be made using 3 letters, 2 numbers, and then 1 letter if all letters and numbers can be repeated? (with replacement) How does your answer change if letters and numbers CANNOT be repeated (without replacement) Use the context of the problem to tell if it is WITH or WITHOUT replacement.
HW- pgs. 416-417 (6.29-6.36)
6.1 & 6.2 Quiz Tuesday 12-4-12 Ch. 6 Test Tuesday 12-11-12 www.westex.org
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