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Chapter 8 - Applying Probability

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This chapter explores the application of probability through simulations, emphasizing that real-life scenarios often extend beyond simple games like tossing coins or rolling dice. It provides practical examples of modeling situations with various outcomes using familiar materials such as cards and dice. The importance of determining adequate trial numbers based on outcome variety is discussed, along with specific examples like scratch-off promotions and real-world decision-making at stop signs. This guide helps illuminate how to effectively simulate probabilities to draw meaningful conclusions.

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Chapter 8 - Applying Probability

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  1. Chapter 8- Applying Probability 4 – Simulations

  2. Simulations • Most real life situations do not involve spinners, • tossing coins or rolling dice....but they’re still useful. • Real life can often be modeled using these materials.

  3. What Material Could You Use If: • There are 2 outcomes? Coin toss • 3 outcomes? Die – group numbers Cards – suit • 4 outcomes? • 6 outcomes? Dice • 13 outcomes? Cards – number • 52 outcomes? Cards – specific card

  4. How Many Trials Should You Do? • Consider the importance of the data. • Consider the number of outcomes: – If a situation only has 2 outcomes, 1000 trials is ridiculous – If a situation has 52 outcomes, 10 trials won’t work

  5. Example #1 • A ‘scratch and win’ promotion at a store allows you to scratch of one box on a card with 13 boxes. A prize is behind one of the boxes. – What is the theoretical probability that you guess the correct box? – What experiment could you design to simulate this experiment? – How many trials would you conduct?

  6. Example #2 • Arriving to a stop sign there is a 1 in 3 chance that there is another car there before you. What is the chance that you get to go immediately? – What is the theoretical probability? – What experiment could you use? – How many trials would you do?

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