1. Review Problem
In my closet, I have 3 caps of baseball teams (NY Yankees, Atlanta Braves, and Nashville Sounds), 2 caps of NFL teams (Patriots, Titans), and 3 caps of NBA teams (2 of the Atlanta Hawks and 1 Boston Celtics). I am having a bad hair day, so I quickly reach in to grab one of my caps. Given that I got a baseball team cap, what is the probability I picked my Braves hat?

2. Homework Review
1. 2/5; 1/ /75; 2/3 6. 3/8; 3/ / /3
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3. Stochastic Processes and Trees
CFU Use a variety of counting methods to organize information, determine probabilities, and solve problems
Stochastic Processes and Trees

4. Stochastic Process
A Stochastic Process is an experiment which consists of a sequence of subexperiments
Includes flipping a coin three times and noting the results. However, it is usually more complicated than that
Best way to work with these? The Tree Diagrams we learned in Chapter 1

5. Probability Measure
The probability measure of an experiment can be obtained by defining the probability of each outcome to be the product of the conditional probabilities assigned to the branches to result in that outcome.
Remember, whenever we see “and” in probability, we generally want to multiply

6. Example
An experiment consists of two steps. First a box is selected from a set of two boxes labeled a and b. Then an urn is selected from the box. Box a contains 3 urns, labeled A, B, and C, and box b contains 2, labeled D and E. Draw a tree diagram to represent outcomes and assign conditional probabilities.
Notice the second stage is Pr(A|a) for the individual outcome

7. Example
Half of the cars at a rental location are Chevys, 1/3 are Fords, and 1/6 are Dodge. Of the Chevys, 2/3 are automatic and the rest manual. Of the Fords, 1/5 are automatic, the rest manual. And of the Dodges, 1/2 are automatic and 1/2 are manual. Draw a tree diagram to represent the probabilities of each outcome
What is the probability of getting a manual car?

8. Classwork/Homework Work on p. 84 #1 – 4, 6 – 12, 14
Once again, remember that tree diagrams can be useful…

9. Further Example
To continue the diagram we had earlier, look at the picture on p. 80 as we are now picking a ball from the urn.
What is the probability that a red ball is drawn? A white ball? A blue ball?

10. Homework Review 3b. 5/9 4. .3 6. 1/8 7. 5/9; 5/6 8. 17/50
9. 19/ ;