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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

Objective: SSBAT find the probability of the complement of events and applications of probability.

Standards: M11.E.3.1.1

slide2

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
slide3

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}
slide4

Examples.

Use the spinner to the right.

Find the probability of not rolling a 5.

P(not 5) =

=

P(not 7 or 8) =

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Use a standard deck of cards.

Find the Probability of not picking a Heart

P(Not Heart)

=

=

or 0.75

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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)

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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.

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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

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Review: Tree Diagram

  • Find the sample space for choosing an outfit from the following.
  • Shirt: Sweater, Blouse, T-Shirt
  • Pants: Jeans or Khakis
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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) =
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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?

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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) =

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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
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Homework

Worksheet 3.1 D