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) = 78

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-ShirtPants: Jeans or Khakis

Example with a Tree Diagram:

1. 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) =

2. A customer has the following options for purchasing a new car.

Manufacturer: Ford, Chevrolet, DodgeDoors: 2 door or 4 doorColors: 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?

Examples with the Fundamental Counting Principle

3. 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) =

4. 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

Homework

Worksheet 3.1 D