introductory statistics lesson 3.1 d
Post on 24-Feb-2016
46 Views
Preview:
DESCRIPTION
TRANSCRIPT
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
top related