Statistics 3502/6304 Prof. Eric A. Suess Chapter 4

Introduction to Probability A measure of uncertainty. Examples: Screening Tests – Pregnancy, Illegal Drugs, Sports Drug Tests Quality Control, Reliability, Six Sigma ESP Probability is the tool used to make inferences in Statistics

What does random mean? That was so random? This statement is past tense. An event is random before is happens. An outcome is random when there are probabilities of the outcomes. Once the event has taken place it is no longer random. We can talk about an outcome being likely or unlikely for a probability model.

Interpretations of Probability Classical Interpretation of Probability Based on counting Developed with games of chance. Flip a coin Draw a card from a shuffled deck of cards Blackjack, roulette, etc.

Interpretations of Probability Relative Frequency Interpretation of Probability Preform and experiment a large number of times and compute the relative frequency of the event. Simulation Observing a production process

Interpretations of Probability Subjective Interpretation of Probability A one-time statement of the likelihood of an event occurring Weather prediction for tomorrow.

Finding Probabilities Using counting. Example: Flip a fair coin twice, what is the probability of HH? Of HT? Example: Draw a card from a shuffled deck of cards, what is the probability of getting a Red card? Getting the King of Harts?

Events and Probability Rules The probability of an event A is between 0 and 1. The event A or B Two events are mutually exclusive if the occurrence of one event excludes the possibility of the occurrence of the other event. Additive Rule for Mutually Exclusive Events: If two events, A and B, are mutually exclusive, the probability of either event occurring is the sum of the probability of each event.

Events and Probability Rules

Conditional Probability: When a probability is computed knowing the occurrence of another event. See Table 4.2 Unconditional Probability: When a probability is computed overall. See Table 4.2

Events and Probability Rules

Bayes’ Rule False Positive False Negative Sensitivity Specificity Prevalence, prior probability Posterior probability Example 4.3 and 4.4