1. INFM 718A / LBSC 705 Information For Decision Making Lecture 7

2. Probability Likelihood that [an outcome] will occur when the uncertainty [related to it] is resolved. We are interested in objective uncertainty in this lecture. Outcomes need to be mutually exclusive and collectively exhaustive.

3. Examples Flipping a coin: 2 possible outcomes (heads or tails), with equal likelihoods, each with a probability of 1/2. Throwing a die: 6 possible outcomes (1,2, 3, 4, 5, 6), with equal likelihoods, each with a probability of 1/6. P (even) = 1/2 P (>2) = 4/6

4. Disjoint and Independent Events Disjoint events: Two (or more) events with no common outcomes. E.g.: P (2 and odd). Independent events: Two (or more) events, where knowing the outcome of one event will not provide any information about the probability of the other event. E.g.: Throwing a die and flipping a coin together.

5. Joint Probability Probability that two independent events will occur together. E.g.: Throw a dice, flip a coin, what is the probability that the die shows 1 and the coin shows heads. P (1 and H) = 1/6 * 1/2 =1/12

6. Conditional Probability Probability of an outcome, under the condition that another, dependent event has had a certain outcome. E.g.: Probability that the die shows 1, based on the information that it shows an odd number. P (1 | odd).

7. Bayes’ Theorem

10. AB

11. In-Class Exercises 4 4.1.a) You can use different approaches: –Enumerate all possible outcomes –Use a numeric approach 4.1.b) Use a combination of approaches 4.1.c) Relate to the previous question, use Bayes’ Theorem

12. Probability Trees A type of visual model to represent joint probabilities. E.g.: A woman has two children. What is the probability that both children are boys?

13. Probability Trees First child is boy First child is girl ½ ½ Second child is boy Second child is girl ¼ ¼ ¼ ¼ Both children are boys

14. Probability Trees In-class Exercise 4.2.

15. Joint Probabilities Textbook example (pp. 228-234) –Blood test In-class Exercise 4.3.

16. Decision Trees Textbook example (pp. 284-297) –Medfly eradication Install TreePlan –BlackBoard > Course Documents > Add-Ins –Download and unzip the file –Open treeplan.xla in Excel In-class Exercise 5.1.