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

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.

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

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.

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

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).

Bayes’ Theorem

AB

In-Class Exercises 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

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?

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

Probability Trees In-class Exercise 4.2.

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

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