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  The complement of event E is denoted by E ′  E ′ is read as “E prime”  P(E) + P(E′) = 1

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}

Examples. 1.Use the spinner to the right. Find the probability of not rolling a 5. P(not 5) = P(not 7 or 8) =

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

3.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)

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.

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

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

2.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 a)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?

Homework Worksheet 3.1 D