Probability is used all of the time in real life Gambling Sports Weather Insurance Medical Decisions Standardized Tests And others Definition of Probability The likelihood of something ID: 693872
Download Presentation The PPT/PDF document "Unit 6: Probability Uses of Probability" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
Slide1
Unit 6: ProbabilitySlide2
Uses of Probability
Probability is used all of the time in real life
Gambling
Sports
Weather
Insurance
Medical Decisions
Standardized Tests
And othersSlide3
Definition of Probability
“The
likelihood of something
happening”
We use this to answer questions like:
What is the chance of rain tomorrow?
Will you win at Black Jack?
Who will win the
S
uper Bowl?
Is the answer A, B, C, or D?
What are the chances of rolling a 13 with 2 dice?Slide4
Basic Probability
Probability is always between 0 and 1
.5Slide5
Random Things to Know
Dice
(singular = “die”)
Most cases: 6 sided
Numbers 1,2,3,4,5,6
Special Cases:
4 sided8 sided10 sided12 sided20 sided
Slide6
Random Things to Know
Cards
Typical Deck: 52 cards
4 Suits (13 cards each)
Clubs Spades
2
-10
2-103 Face 3 Face1 Ace 1 Ace Hearts Diamonds2-10 2-10
3 Face 3 Face1 Ace 1 AceSlide7
Random Things to Know
License Plates
7 Characters
Different states
have different
rules
Slide8
Counting Principle
If you have 6 shirts and 3 pants how many different outfits can you create?Slide9
Counting Principle
If you have M of one option
a
nd you have N of another option,
Then there are
ways of doing both
M = shirts
N = pantsNumber of outfits you can make =
Slide10
Counting Principle
When flipping a coin 15 times how many results are possible?
*Think how many different results are there when you flip a coin*Slide11
Counting Principle
A restaurant has on its menu
5 choices for appetizers
3 choices for main course
2 choices for dessert
How many different meals (appetizer, main course, and dessert) can you choose?Slide12
Factorials!
Slide13
Multiplication Rule and
Addition Rule of ProbabilitySlide14
Multiplication Rule and
Addition Rule of Probability
Examples
What is the probability of rolling a 6 on a die
and
then rolling another 6?
so
What is the probability rolling a 1
or
a 2 on a single roll of a die?
so
Slide15
Combinations
If you have 5 trophies but only space on a shelf for 2 of them how many different ways can you arrange your trophies?
BIG QUESTION: DOES ORDER MATTER??Slide16
Combinations
Remember the Counting Principle:
M*N = total number of ways to select items
How many trophies can you choose between?
5
How many spots are there?
2
So… Slide17
Combinations
Def
: A way of selecting items where the order
does not
matter
If you order pizza it doesn’t matter if you tell them
“Peperoni, Pineapple, and Sausage” or
“Sausage, Peperoni, and Pineapple” NO! It all goes on the pizza! The order doesn’t matterSlide18
Combinations
n = total number of elements
r = number of items chosen
Slide19
Permutations
You and your 3 friends are standing in line to buy tickets to a movie. How many ways are there for you to arrange yourselves?Slide20
Permutations
Remember the Counting Principle:
M*N = total number of ways to select
items
How many choices do you have for the first spot?
(4)
How many choices do you have for the second spot? (3)
How many choices do you have for the third spot? (2) How many choices do you have for the fourth spot? (1)So Slide21
Permutations
Def
: A way of selecting items where the order
does
matter
In races who comes in 1
st
, 2nd, and 3rd is very important for prizes, and rankings. The order does matter.Slide22
Permutations
If repetition is not allowed:
If repetition is allowed:
n = total number of elements
r = number
chosen