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Exploring Sample Spaces and the Counting Principle in Probability

This lesson focuses on creating and utilizing sample spaces while applying the counting principle in probability. Students will work through various examples, including rolling dice, tossing coins, and making sandwich choices, to conceptualize how to organize outcomes and compute probabilities. Key exercises involve determining sample spaces for actions like rolling two number cubes and tossing coins, and calculating probabilities for specific events, such as rolling a sum of 8 or getting two heads. Homework includes exercises that reinforce skills learned in class.

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Exploring Sample Spaces and the Counting Principle in Probability

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  1. Lesson 12-3 Sample Spaces

  2. Obj: To make and use sample spaces and to use the counting principle • HWK: p 593 2-28 even • Vocab: 1) sample space • 2) counting principle

  3. Key Concepts: The Counting Principle • Suppose there are m ways of making one choice and n ways of making a second choice. Then there are m x n ways to make the first choice followed by the second choice

  4. Ex 1) a) Make a table to find the sample space for rolling 2 number cubes • b) Find P(at least one 3) • c) Find P(sum of 8) • d) Find P(doubles)

  5. Ex 2) Find the sample space for tossing two coins. Find P(2 H’s)

  6. Ex 3) Suppose you are going to travel on a river. You have two choices of boats – a kayak or a rowboat. You can go upstream on three smaller streams – to the north, northwest or northeast. • a) Write the sample space for your journey • b) Find P(R, N) =

  7. Ex 4) Deli Counter a) How many different sandwiches • Fresh Breads Deli Meats can you order when you choose • Rye Roast Beef one bread and one meat? • Wheat Turkey • White Ham • Pita Pastrami b) If chicken is added to the meats • Wrap Salami how many sandwiches? • Liverwurst • c) Find P(Rye) • Find P(Ham)

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