1. Probability and Simulation The Study of Randomness

2. Probability Probability is the branch of mathematics that describes the pattern of chance outcomes.

3. Probability Jargons Experiment: process of measuring or observing an activity for the purpose of collecting data. Ex: rolling a pair of dice Outcome: A particular result of an experiment. Ex: rolling a pair of threes with the dice. Sample Space: All possible outcomes in an experiment. Ex: sample space of a die {1, 2, 3, 4, 5, 6} Event: One or more outcomes that are of interests for the experiment. Ex: rolling a total of 2, 3, 4, or 5 with 2 dice

4. Basic Set Notations sample space.S Suppose that you roll a die once. There will be 6 possible outcomes; you may get either 1, 2, 3, 4, 5 or 6. These possible outcomes of such a random experiment are called the basic outcomes. The set of all basic outcomes is called the sample space. The symbol S will be used to denote the sample space. S = sample space

5. What is the sample space for a roll of a single six-sided die? S = {1, 2, 3, 4, 5, 6} What is the sample space for tossing a coin? S = { T, H}

6. Classical Probability Refers to the situation when we know the number of possible outcomes of the event of interest and can calculate the probability of that event. P[A]= Number of possible outcomes in which EVENT A occurs Number of possible outcomes in the SAMPLE SPACE

7. Event A = rolling a total of 2, 3, 4, or 5 P[A]=? A = 10 S = 36 P[A]= 10/36 = 0.28

8. Classwork Find the Probability of the following events A = same number B = both odd number C = sum of 7, 8, 9, or 10 D = an odd and an even number E = not getting a sum of even number 17% 25% 50% 50% 50%