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Introductory Statistics Lesson 3.1 D

Introductory Statistics Lesson 3.1 D Objective: SSBAT find the probability of the complement of events and applications of probability. Standards: M11.E.3.1.1. Complement of Event E The set of all outcomes in a sample space that are NOT included in event E

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Introductory Statistics Lesson 3.1 D

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  1. Introductory Statistics Lesson 3.1 D Objective: SSBAT find the probability of the complement of events and applications of probability. Standards: M11.E.3.1.1

  2. Complement of Event E • The set of all outcomes in a sample space that are NOT included in event E • The complement of event E is denoted by E′ • E′ is read as “E prime” • P(E) + P(E′) =1

  3. Example: • Roll a die and let E be the event of rolling a 1 or 2. • E′ would then be rolling a 3, 4, 5, 6 • E = {1, 2} • E′ = {3, 4, 5, 6}

  4. Examples. Use the spinner to the right. Find the probability of not rolling a 5. P(not 5) = = P(not 7 or 8) =

  5. Use a standard deck of cards. Find the Probability of not picking a Heart P(Not Heart) = = or 0.75

  6. You put all the letters of the alphabet in a hat. You randomly pick one letter from the hat. What is the probability that you do not pick a vowel? (there are 5 vowels in the alphabet)

  7. Sometimes you will have to use a Tree Diagram or the Fundamental Counting Principle to find the total number in the sample space first before finding the probability.

  8. Review: Fundamental Counting Principle • How many ways can a committee of 5 people be chosen from a group of 30 people? • ____ ____ ____ ____ ____ 30 · 29 · 28 · 27 · 26 = 17,100,720 17,100,720 different ways

  9. Review: Tree Diagram • Find the sample space for choosing an outfit from the following. • Shirt: Sweater, Blouse, T-Shirt • Pants: Jeans or Khakis

  10. Example with a Tree Diagram: • Samantha tosses 3 dimes into the air. What is the Probability of Exactly 2 Heads. • Make a tree diagram to show the possible outcomes • Possible Outcomes: {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT} • P(2 Heads) =

  11. A customer has the following options for purchasing a new car. • Manufacturer: Ford, Chevrolet, Dodge • Doors: 2 door or 4 door • Colors: Red, Black, Silver • What is the probability that the next car sold is a 4 door? • Find the possible outcomes using tree diagram. b) What’s the probability that the next car sold is a Red Chevy?

  12. Examples with the Fundamental Counting Principle The daily number in the PA lottery consists of 3 numbers. Each number can be from 0 to 9 and the numbers may repeat. If you randomly choose a 3 digit number to play, what is the probability you will pick the winning number?  Find how many possible outcomes there are  10 · 10 · 10 = 1,000  P(winning) =

  13. You roll 2 dice. • What is the probability of getting the same number on each die. •  Make a tree diagram showing the possible outcomes • P(Same #) = • P(Same #) = or 0.167

  14. Homework Worksheet 3.1 D

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