1. Probability and Simulation GENERATING SAMPLE SPACE

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

3. Three Children 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. 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. List all possible orderings for the 3 children. EXAMPLE

4. Enumeration 1 st Child 2 nd Child 3 rd Child BBB GBB BGB BBG GGB GBG BGG GGG S={BBB, GBB, BGB, BBG, GGB, GBG, BGG, GGG}

5. Tree Diagrams 1 st Child __ 2 nd Child __ 3 rd Child BBB B G B G B G BBG BGB BGG GBB GBG GGB GGG B G B G B G B G 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) P(of getting a boy then a girl) P(of getting all boys) P(of having a girl as a third child) P(of having 2 girls) =2.5 =.25 =.125 =.50 =.375

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? 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. 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 NOTE!

9. Organize a list of possible outcomes when you toss a coin 4 times T T T T H T T T H H T T H H H T HHHH T H T T H T H T H H T H T T H T H T T H H T H H T T T H T H H T T H H H T H T H T T H H 0 heads 1 head 2 heads 3 heads 4 heads

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. 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 WHICH ONE ARE YOU?