1. STAT 1301 Introduction to Probability

2. Statistics: The Science of Decision Making in the Face of Uncertainty l Uncertainty makes life challenging and interesting –very few things are absolutely certain

3. Chance Situations  Flip coin -- What is the chance of heads?  What is the chance that SMU’s football team wins the rest of its games?  Weather tomorrow -- Rain? Mathematical treatment of chance has roots in gambling. Games of chance are ideal examples.

4. (1) Classical (Theoretical) l Chance situation - - N = total number of possible occurrences (equally likely) X = number of occurrences which result in outcome Chance[outcome] = x 100% 3 Ways to Calculate Chance N X

7. Drop Thumbtack Chance it lands “point down” = ?

8. (2) Frequency (Long Run) l Chance of an outcome is the percent of times the outcome occurs when the procedure is repeated over and over, independently and under the same conditions. 3 Ways to Calculate Chance

9. (3) Subjective (Degree of Belief)

10. Virtual Impossibility Virtual Certainty Chance = 0% Chance = 100% Probability = 0 Probability = 1 Facts About Chance Probability is chance expressed as a fraction

11. Chance[ outcome does not occur ] = 100% - Chance[ outcome does occur ] IN GENERAL: Chance[ something ] =100% - Chance[ opposite ] Probability[ something ] =1 - Probability[ opposite ]

14. l Random drawing with replacement –after each draw, the ticket selected is placed back into the box l Random drawing without replacement –after each draw, the ticket selected is not placed back into the box

16. Conditional Probability The probability that something will happen given the information that a first thing has in fact happened. Notation: P r [ outcome 2 | outcome 1 ] “The conditional probability that outcome 2 occurs given that outcome 1 has occurred.” “given”

17. Conditional Probability The probability that something will happen given the information that a first thing has in fact happened. Drawing without replacement example: Pr(2nd Red | 1st Red) = 1/5

19. Unconditional Probability NOTE: The “standard” probability without a condition is called the unconditional probability.

20. Multiplication Rule The Chance that two things will BOTH happen equals the chance that the first will happen, multiplied by the chance that the second will happen given that the first has happened. (Text, p. 229) Pr[ first AND second ]=Pr[ first ] x Pr[second | first ] Careful !! -- Multiply probabilities and convert to chance