1. STATISTICS 5.0 Introduction to Probability “Basic Probability Theory” 5.0 Introduction to Probability “Basic Probability Theory” STATISTICS “Basic Probability Theory” 5.0 Introduction to Probability STATISTICS “Basic Probability Theory”

2. 5.0 Introduction to Probability Terms widely used in probability: – Experiment → The process of measuring/observing an activity for the purpose of collecting data. Example: Rolling a pair of dice. – Outcome → A particular result of an experiment. Example: Rolling pair of dice with 3s with the dice – Sample Space → All possible outcomes of the experiment. Example: Sample space of rolling a pair of dice. {2,3,4,5,6,7,8,9,10,11,12} – Event → One or more outcomes that are of interest for the experiment and which is/are subset of the sample data. Example: Rolling a pair of a 2,3,4 or 5 with the 2 dice

3. CLASSICAL PROBABILITY 1.Refers to situation when we know the number of possible outcomes of the event of interest. 2.Can calculate the probability of that event with the following equation: P[A] = Number of possible outcomes in which Event A occurs Total number of possible outcomes in the sample space 5.0 Introduction to Probability

4. CLASSICAL PROBABILITY Examples: 1.Probability: sex of a new born baby 2.Probability: number 6 from throw of a dice 3.Probability: State that will Malaysia Cup 5.0 Introduction to Probability

5. EMPIRICAL PROBABILITY 1.Practice when don’t know enough about the underlying process to determine the number of outcomes associated with the event 2.Requires that you count the frequency that an event occurs through an experiment and calculate the probability from the relative frequency distribution. P[A] = Frequency in which Event A occurs Total number of observations 5.0 Introduction to Probability

6. EMPIRICAL PROBABILITY Examples: 1.Probability: Number of student that will score 4 flat next semester 2.Probability: Number of student that get barred for the semester 3.Probability: Number of student intake 5.0 Introduction to Probability

7. SUBJECTIVE PROBABILITY 1.Is used when classical and empirical probabilities are not available. 2.Under these circumstances, we rely on expertise, experience and instinct to estimate the probabilities 5.0 Introduction to Probability

8. SUBJECTIVE PROBABILITY Examples: 1.Probability: Sir Faiz will play with Man Utd 2.Probability: Malaysia will win the world cup 3.Probability: MAS ans Air Asia will merge 5.0 Introduction to Probability

9. Basic Properties of Probability 1.If P[A] = 1, then Event A must occur with certainty 2.If P[A] = 0, then Event A will not occur with certainty 3.The probability of Event A must be between 0 and 1. 4.The sum of all the probabilities for the events in the sample space must be equal to 1 5.The complement to event A is defined as all the outcomes in the sample space that are not part of event A and is denoted as A’. Using this definition, we can state the following: P[A] + P[A’] = 1; P[A]=1- P[A’] 5.0 Introduction to Probability

10. The Intersection of Events 1.The intersection of Event A and B represents the numbers of instances where Event A and Event B occur at the same time. Denote as P[A∩B] = P[A and B] 2.The probability of the intersection of 2 events is known as a joint probability. 5.0 Introduction to Probability

11. The Union of Events 1.The union of Event A and B represents all the instances where Event A or Event B or both occur at the same time. Denoted as P[AuB] = P[A or B] 2.The probability of the intersection of 2 events can never be more than the probability of the union of 2 events. 5.0 Introduction to Probability