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Probability and Simulation

Probability and Simulation. The Study of Randomness. Listing All Possible Outcomes of a Probabilistic Experiment. Enumeration Tree diagrams Additional methods – counting fundamentals. Three Children Example. Homework.

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Probability and Simulation

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  1. Probability and Simulation • The Study of Randomness

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

  3. Three Children Example Homework • 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. 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 exactly 2 girls) PRACTICE:Using the previous conditions, what is the probability of these events from happening? =3/8 =4/8 or 1/2 =1/8 =4/8 or 1/2 =3/8

  7. Warm-up 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] = .27 P[green] = .23 P[blue] = .36 P[yellow] = .14

  8. P(rain) = 25% P’(rain) = 75% Compliment of a probability The chances of raining today is 25%. What is the probability that it’s NOT going to rain today?

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