Probability and Simulation

1. Probability and Simulation • GENERATING SAMPLE SPACE

2. Listing All Possible Outcomes of a Probabilistic Experiment • Enumeration • Tree diagrams • Additional methods – counting fundamentals

3. Three Children Example EXAMPLE • A couple wants to have exactly 3 children.  Assume that each child is either a boy or a girl and that each is a single birth.  • List all possible orderings for the 3 children.

4. Enumeration S={BBB, GBB, BGB, BBG, GGB, GBG, BGG, GGG}

5. B B B B B B B G G G G G G G Tree Diagrams 1st Child __ 2nd Child __ 3rd Child BBB BBG BGB BGG GBB GBG GGB GGG S={BBB, BBG, BGB, BGG, GBB, GBG, GGB, GGG}

6. PRACTICE:Using the previous conditions, what is the probability of these events from happening? P(of getting 2 consecutive boys) =2.5 P(of getting a boy then a girl) =.25 P(of getting all boys) =.125 P(of having a girl as a third child) =.50 =.375 P(of having 2 girls)

7. A glass jar contains 6 red, 5 green, 8 blue and 3 yellow marbles. If a single marble is chosen at random from the jar, what is the probability of choosing a red marble? a green marble? a blue marble? a yellow marble? P[red] = .27P[green] = .23P[blue] = .36P[yellow] = .14

8. NOTE! Being able to properly enumerate the outcomes in a sample space will be critical in determining probabilities. Enumeration and tree diagram will be very helpful to eliminate in accidentally overlooking any outcomes

9. Organize a list of possible outcomes when you toss a coin 4 times

10. Multiplication Principle: If you can do one task in x1 number of ways and a second task in x2 number of ways, then both can be done in (x1) (x2) number of ways Example: Sample space of tossing a coin 3 times: 2 x 2 x 2 = 8

11. WHICH ONE ARE YOU? Odds For Meeting A FemaleThe probability of a young man meeting a desirable and receptive young female increases by exponential progression when he is already in the company of: (1) a date (2) his wife (3) a better looking and richer male friend