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5/10 Adv. Alg/Trig Bell Ringer

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?

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5/10 Adv. Alg/Trig Bell Ringer

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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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