1. MATH 1107 Elementary Statistics Lecture 4 Introduction to Probability

2. Who is George Bush’s favorite friend? –Monica –Phoebe –Rachel –Joey –Chandler –Ross How many times has Dr. Priestley jumped out of an airplane? –0 –1 –2 –3 or more

3. Introduction to Probability Unless you have insight into these questions, you would have to guess randomly. Therefore, the probability that you are correct is 1/6 or 16.67% for the first question and ¼ or 25% for the second question.

4. Introduction to Probability Terms used in analysis of probabilities: experiment event (represented by a capital letter – p(A)) sample space

5. Introduction to Probability Using a deck of cards as an example: Pulling a card from the deck is an experiment The card selected represents the event Each individual card together represents the sample space. Describe the probability of selecting a heart  Sample Space = {H,S,D,C}  P(H) = ¼ Describe the probability of selecting the Jack of Clubs  Sample Space = {2H, 3H, 4H…JC, QC, KC}  P(JC) = 1/52

6. Introduction to Probability Events in a Sample Space must be mutually exclusive and collectively exhaustive. Using a fair die, develop the sample space ensuring that all events are mutually exclusive and collectively exhaustive. What are two events in a die experiment that are mutually exclusive? What are their individual and collective probabilities?

7. Introduction to Probability In Class exercise: An experiment consists of flipping a fair coin three times. Compute the probabilities of the following events: (A)Exactly one head will appear (B)At least one head will appear (C)Tails never comes up

8. Step 1: Compute the mutually exclusive, collectively exhaustive sample space: HHHTHHHTHTHT HTTTTHHHTTTT Step 2: Determine how many ways each event can occur: A: HTT, THT, TTH B: HHH, HTH, HTT, HHT, THH, THT, TTH C: HHH Step 3: Divide the number of possibilities for each event by the total number in the sample space: A: 3/8 = 37.5 B: 7/8 = 87.5 C: 1/8 = 12.5 Introduction to Probability

9. In Class exercise: A pair of fair dice are rolled. Compute the following events: (A)The sum of the two dice is 7 (B)The sum of the two dice is 5 (C) The sum of the two dice is even

10. Step 1: Compute the mutually exclusive, collectively exhaustive sample space: {(1,1), (1,2), (1,3)…(6,4), (6,5), (6,6)} Step 2: Determine how many ways each event can occur: A: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) B: (1,4), (2,3), (3,2), (4,1) C: (1,1), (1,3), (1,5)…(6,2), (6,4), (6,6) Step 3: Divide the number of possibilities for each event by the total number in the sample space: A: 6/36 = 16.67% B: 4/36 = 11.11% C: 18/36 = 50% Introduction to Probability

11. Another way to discuss probabilities is in terms of “odds”. Odds are stated as the ratio of the probability of an event occurring and the probability of an event not occurring. The odds of P(A) occurring is stated as: P(A)/P(B) or b:a. Note that the event in question occurring is always stated second. Odds are generally used in gambling, lotteries, etc because it is a convenient way to describe the payoffs.

12. Duke 4:1 Maryland 5:1 Kansas 5:1 Cincinnati 7:1 Oklahoma 8:1 Introduction to Probability For example, the commonly accepted odds for the top five teams to win the 2003 NCAA tournament were: