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Understanding Probability with Dice: Total Outcomes and Event Calculation

In this lesson, we explore the concept of probability using the rolling of three dice. According to the Fundamental Counting Principle, the total possible outcomes when rolling three dice at once can be calculated. We'll also review examples involving one pair of dice, focusing on determining the probability of specific events such as rolling doubles. Our goal is to grasp compound events using tree diagrams and develop skills to calculate desired probabilities in various scenarios. Complete the independent practice assigned for further mastery.

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Understanding Probability with Dice: Total Outcomes and Event Calculation

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  1. 5/11 Adv. Alg/Trig Bell Ringer You roll three dice one time. How many total possible outcomes for this situation? HINT: Use Fundamental Counting Principle. HOMEWORK: Finish Today’s Independent Practice

  2. 5/11 News and Notes • Perfection: 2nd Period • Review Tomorrow • Quiz Friday

  3. Today’s Goal • YESTERDAY: Use tree diagrams to determine sample space. • TODAY: Calculate probability of compound events using tree diagrams

  4. Quick Review from Yesterday – HW #2 • A pair of dice is rolled once. How many possible outcomes are there? Dice 1 = 6 outcomes Dice 2 = 6 outcomes Together = 6 x 6 = 36 TOTAL OUTCOMES

  5. Yesterday is Step 1 of Today. • Step 1: Determine Total Possible Outcomes So, we have 36 total outcomes. Today’s additional question: What’s the probability that you roll doubles? • Step 2: Determine # of events that satisfy your desired outcome.

  6. How many doubles are there? • {1,1; 2,2; 3,3; 4,4; 5,5; 6,6} = 6 DESIRED OUTCOMES • Step 3: Calculate desired probability  “desired/total possible” = 6 / 36 = 0.1666667

  7. Example 2 • What’s the probability that your meal includes meat?

  8. Total Outcomes = 18 • Desired outcomes = 12 • P(Meat) = 12 / 18 = 0.67

  9. Guided Practice • Finish your paper from yesterday by answering the following questions: 1. What is the probability thata baby girl will have a name (first or middle) where the last letter is E or A? 2. What is the probability that your child’s name will have an E as the first letter of one of the names?

  10. Exit Ticket – Sit quietly for credit A fair coin is tossed 3 times. What is the probability of you getting exactly 2 heads? • 0.25 • 0.125 • 0.325 • 0.67 HOMEWORK: Finish Today’s Independent Practice

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