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Probability and Sample Space: Algebra and Trigonometry Bell Ringer Activity

This bell ringer activity focuses on calculating probabilities and sample spaces, using tree diagrams and the Fundamental Counting Principle. It includes examples with lunch combos and baby names, guiding students through independent practice.

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Probability and Sample Space: Algebra and Trigonometry Bell Ringer Activity

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  1. 5/10 Adv. Alg/Trig Bell Ringer The ratio of male teachers to female teachers at Bogan is 2:3. If one teacher is randomly selected to win a $25,000 bonus, what is the probability the winner is female? Is the following independent or dependent: if a 2nd winner was selected, what’s the probability they are female? HOMEWORK: Finish Today’s Independent Practice

  2. 5/10 News and Notes • Perfection: 8th Period • Missing Quizzes: • 2nd: Octavia • 4th: Jasmine, Monica, Taunjear. • Posse today after school • Quiz Friday

  3. Today and Tomorrow • TODAY: Use tree diagrams to determine sample space. • TOMORROW: Calculate probability of compound events using tree diagrams

  4. Def: Sample Space • Total number of outcomes • Simple example: Roll a dice, what’s the sample space? • {1, 2, 3, 4, 5, 6}  6 total outcomes.

  5. Example #1 • A new restaurant has opened and the offer lunch combos for $5.00. With the meal you get 1 sandwich, 1 side and 1 drink. The choices are below: Sandwiches: Chicken Salad, Turkey, Grilled Cheese Sides: Chips, Fries, Fruit Drinks: Soda, Water What is the total number of outcomes possible?

  6. Sandwiches: Chicken Salad, Turkey, Grilled Cheese Sides: Chips, Fries, Fruit Drinks: Soda, Water Step 1: How many outcomes for each? Sandwiches: 3 Sides: 3 Drinks: 2

  7. Step 2: Start tree with first round (Sandwich)

  8. Step 3: Branch off each of first with # of 2nd outcome (sides)

  9. Step 4: Place 3rd outcome (Drink) off each of 2nd.

  10. Step 5: COUNT OUTCOMES SAMPLE SPACE = 18 OUTCOMES

  11. Is there an easier way to get 18? • We said: Outcome #1 = 3 options Outcome #2 = 3 options Outcome #3 = 2 options How does this get us to 18?

  12. Fundamental Counting Principle • If you have a ways of doing event 1, bways of doing event 2, and cways of doing event 3, then you can find the total number of outcomes by multiplying: a*b*c • So, in our example, we had 3, 3, and 2, so … 3*3*2 = 18 outcomes

  13. When do you need a tree? • Tree diagram if you’re interested in specific outcomes. • FCP if you’re only interested in the total.

  14. Guided Practice: With Partner • You each get a blank piece of paper. On the paper you must have: • Fundamental Counting Principle and explanation. • Tree diagram. • Answer to both questions. ** When you finish, start independent practice.

  15. Guided Practice: The problem • A survey at a hospital showed the most popular names for baby girls are: Emily, Haley, Kayla, and Samantha. • The most popular middle names are Anne, Marie and Elizabeth. Q1: How many possible names can be generated using the first and middle names given? Q2: What is the probability that a baby girl will be named Emily Elizabeth if her parents choose from this sample space?

  16. Exit Ticket: SIT QUIETLY FOR CREDIT! You are taking a test that has five True/False questions.  If you answer each question with True or False and leave none of them blank, in how many ways can you answer the whole test? SHOW WORK! • 5 • 10 • 25 • 32 HOMEWORK: Finish Today’s Independent Practice

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