Probability, Permutations, & Combinations · Permutation & Combination Permutation OR Combination 9...
Transcript of Probability, Permutations, & Combinations · Permutation & Combination Permutation OR Combination 9...
![Page 1: Probability, Permutations, & Combinations · Permutation & Combination Permutation OR Combination 9 a. Arrangement of 10 books on a shelf b. Committee of 3 people out of a group of](https://reader034.fdocuments.in/reader034/viewer/2022050807/600b41258b4e403c6102799d/html5/thumbnails/1.jpg)
Probability, Permutations,
& CombinationsLESSON 11.1
![Page 2: Probability, Permutations, & Combinations · Permutation & Combination Permutation OR Combination 9 a. Arrangement of 10 books on a shelf b. Committee of 3 people out of a group of](https://reader034.fdocuments.in/reader034/viewer/2022050807/600b41258b4e403c6102799d/html5/thumbnails/2.jpg)
Objective
• Define probability
• Use the counting principle
• Know the difference between combination and
permutation
• Find probability
![Page 3: Probability, Permutations, & Combinations · Permutation & Combination Permutation OR Combination 9 a. Arrangement of 10 books on a shelf b. Committee of 3 people out of a group of](https://reader034.fdocuments.in/reader034/viewer/2022050807/600b41258b4e403c6102799d/html5/thumbnails/3.jpg)
Probability
PROBABILITY: the measure of the likeliness of an event
# 𝑜𝑓 𝑤𝑎𝑦𝑠 𝑡𝑜 𝑤𝑖𝑛
# 𝑜𝑓 𝑤𝑎𝑦𝑠 𝑡𝑜 𝑝𝑙𝑎𝑦
![Page 4: Probability, Permutations, & Combinations · Permutation & Combination Permutation OR Combination 9 a. Arrangement of 10 books on a shelf b. Committee of 3 people out of a group of](https://reader034.fdocuments.in/reader034/viewer/2022050807/600b41258b4e403c6102799d/html5/thumbnails/4.jpg)
Probability
1a. What is the probability of rolling a 4 on a 6-sided
die?
1b. What is the probability of rolling an even number
on a 6-sided die?
![Page 5: Probability, Permutations, & Combinations · Permutation & Combination Permutation OR Combination 9 a. Arrangement of 10 books on a shelf b. Committee of 3 people out of a group of](https://reader034.fdocuments.in/reader034/viewer/2022050807/600b41258b4e403c6102799d/html5/thumbnails/5.jpg)
Probability
2. A bag of candy contains 12 red, 11 yellow, 5
green, 6 orange, 5 blue, and 16 brown candies.
a.) What is the probability that you will randomly draw a yellow
candy from the bag?
b.) What is the probability that you will NOT draw an orange candy
from the bag?
![Page 6: Probability, Permutations, & Combinations · Permutation & Combination Permutation OR Combination 9 a. Arrangement of 10 books on a shelf b. Committee of 3 people out of a group of](https://reader034.fdocuments.in/reader034/viewer/2022050807/600b41258b4e403c6102799d/html5/thumbnails/6.jpg)
Sample Space
Sample Space is a visual representation of all possible outcomes.
3a. We are going to flip a coin 3 times. Find the
sample space.
![Page 7: Probability, Permutations, & Combinations · Permutation & Combination Permutation OR Combination 9 a. Arrangement of 10 books on a shelf b. Committee of 3 people out of a group of](https://reader034.fdocuments.in/reader034/viewer/2022050807/600b41258b4e403c6102799d/html5/thumbnails/7.jpg)
Sample Space
3b. How many outcomes give us at least 2 heads?
3c. Find the probability of getting at least 2 heads.
![Page 8: Probability, Permutations, & Combinations · Permutation & Combination Permutation OR Combination 9 a. Arrangement of 10 books on a shelf b. Committee of 3 people out of a group of](https://reader034.fdocuments.in/reader034/viewer/2022050807/600b41258b4e403c6102799d/html5/thumbnails/8.jpg)
Permutation & Combination
If a sample set is too large to list, the number of
outcomes and successes can be determined using
permutations and combinations.
Permutations – ORDER MATTERS
Combinations – order DOES NOT matter
![Page 9: Probability, Permutations, & Combinations · Permutation & Combination Permutation OR Combination 9 a. Arrangement of 10 books on a shelf b. Committee of 3 people out of a group of](https://reader034.fdocuments.in/reader034/viewer/2022050807/600b41258b4e403c6102799d/html5/thumbnails/9.jpg)
Permutation
Permutation – ORDER MATTERS
To calculate the number of permutations, multiply
the number of choices possible for each position.
This is called the Counting Principle.
![Page 10: Probability, Permutations, & Combinations · Permutation & Combination Permutation OR Combination 9 a. Arrangement of 10 books on a shelf b. Committee of 3 people out of a group of](https://reader034.fdocuments.in/reader034/viewer/2022050807/600b41258b4e403c6102799d/html5/thumbnails/10.jpg)
Permutation
4a. On a 3-question multiple choice quiz, how many
different quizzes could be turned in if there are 4
options (a,b,c,d)?
4b. How many different quizzes could be turned in if
no answers were repeated?
![Page 11: Probability, Permutations, & Combinations · Permutation & Combination Permutation OR Combination 9 a. Arrangement of 10 books on a shelf b. Committee of 3 people out of a group of](https://reader034.fdocuments.in/reader034/viewer/2022050807/600b41258b4e403c6102799d/html5/thumbnails/11.jpg)
Permutation
To calculate permutation without repetition:
𝑛𝑃𝑟 = 𝑃 𝑛, 𝑟 =𝑛!
𝑛 − 𝑟 !where “n” is the number of objects to choose from
and “r” is the number of object being selected.
![Page 12: Probability, Permutations, & Combinations · Permutation & Combination Permutation OR Combination 9 a. Arrangement of 10 books on a shelf b. Committee of 3 people out of a group of](https://reader034.fdocuments.in/reader034/viewer/2022050807/600b41258b4e403c6102799d/html5/thumbnails/12.jpg)
Permutation
Permutations can be calculated with a calculator.
a) Type the value of “n”
b) [MATH] → PRB → nPr
c) Type the value of “r” and press enter
TRY IT!
5a. P(5,3) b. P(16,5) c. P(25,13)
![Page 13: Probability, Permutations, & Combinations · Permutation & Combination Permutation OR Combination 9 a. Arrangement of 10 books on a shelf b. Committee of 3 people out of a group of](https://reader034.fdocuments.in/reader034/viewer/2022050807/600b41258b4e403c6102799d/html5/thumbnails/13.jpg)
Combination
Combination – order DOES NOT matter,
*object may be repeated
𝑛𝐶𝑟 = 𝐶 𝑛, 𝑟 =𝑛!
𝑛 − 𝑟 ! 𝑟!
![Page 14: Probability, Permutations, & Combinations · Permutation & Combination Permutation OR Combination 9 a. Arrangement of 10 books on a shelf b. Committee of 3 people out of a group of](https://reader034.fdocuments.in/reader034/viewer/2022050807/600b41258b4e403c6102799d/html5/thumbnails/14.jpg)
Combination
Combinations can be calculated with a calculator.
a) Type the value of “n”
b) [MATH] → PRB → nCr
c) Type the value of “r” and press enter
TRY IT!
6a. C(5,3) b. C(16,5) c. C(25,13)
![Page 15: Probability, Permutations, & Combinations · Permutation & Combination Permutation OR Combination 9 a. Arrangement of 10 books on a shelf b. Committee of 3 people out of a group of](https://reader034.fdocuments.in/reader034/viewer/2022050807/600b41258b4e403c6102799d/html5/thumbnails/15.jpg)
Combination
7. Mrs. Mann is picking 4 students to be team
leaders. There are 25 students in the class. How
many different ways can she pick the 4 students?
![Page 16: Probability, Permutations, & Combinations · Permutation & Combination Permutation OR Combination 9 a. Arrangement of 10 books on a shelf b. Committee of 3 people out of a group of](https://reader034.fdocuments.in/reader034/viewer/2022050807/600b41258b4e403c6102799d/html5/thumbnails/16.jpg)
Combination
8. Super Generic Ice Cream Shoppe has 9 different
flavors to put in your ice cream. You can choose 3
flavors to put in a single dish. How many different
flavor combinations can you create?
![Page 17: Probability, Permutations, & Combinations · Permutation & Combination Permutation OR Combination 9 a. Arrangement of 10 books on a shelf b. Committee of 3 people out of a group of](https://reader034.fdocuments.in/reader034/viewer/2022050807/600b41258b4e403c6102799d/html5/thumbnails/17.jpg)
Permutation & Combination
Permutation OR Combination
9 a. Arrangement of 10 books on a shelf
b. Committee of 3 people out of a group of 10
c. Class presidency – 1st is president, 2nd is VP, etc.
d. Draw a hand of 6 cards from a deck of cards
e. Number of ways to make a license plate
![Page 18: Probability, Permutations, & Combinations · Permutation & Combination Permutation OR Combination 9 a. Arrangement of 10 books on a shelf b. Committee of 3 people out of a group of](https://reader034.fdocuments.in/reader034/viewer/2022050807/600b41258b4e403c6102799d/html5/thumbnails/18.jpg)
Permutation & Combination
THINK!
• Identify if order matters or doesn’t matter FIRST
• Permutations can use the counting principle,
combinations don’t
• Generally: Two things at once – Combination
One after the other - Permutation
![Page 19: Probability, Permutations, & Combinations · Permutation & Combination Permutation OR Combination 9 a. Arrangement of 10 books on a shelf b. Committee of 3 people out of a group of](https://reader034.fdocuments.in/reader034/viewer/2022050807/600b41258b4e403c6102799d/html5/thumbnails/19.jpg)
Permutation & Combination
10. There are 6 students presenting projects in a
history class. The teacher is randomly determining
the order in which the students will present. Each
student only presents once. Brooke is one of the six
students. What is the probability that Brooke will
present first?
![Page 20: Probability, Permutations, & Combinations · Permutation & Combination Permutation OR Combination 9 a. Arrangement of 10 books on a shelf b. Committee of 3 people out of a group of](https://reader034.fdocuments.in/reader034/viewer/2022050807/600b41258b4e403c6102799d/html5/thumbnails/20.jpg)
Compound Probabilities
If more then 1 event is happening, it creates a
Compound Probability.
If independent - P A𝑎𝑛𝑑B = P A ⋅ P(B)
If dependent - P A𝑎𝑛𝑑B = P A ⋅ P(B𝑓𝑜𝑙𝑙𝑜𝑤𝑖𝑛𝑔A)
![Page 21: Probability, Permutations, & Combinations · Permutation & Combination Permutation OR Combination 9 a. Arrangement of 10 books on a shelf b. Committee of 3 people out of a group of](https://reader034.fdocuments.in/reader034/viewer/2022050807/600b41258b4e403c6102799d/html5/thumbnails/21.jpg)
Compound Probabilities
11. From a deck of 52 cards, 3 cards are randomly
chosen. They are a 10, Jack, and another 10, in that
order.
a. Find the probability that this event occurs if each
card is replaced after drawn.
b. Find the probability that this even occurs if each
card is NOT replaced each time.
![Page 22: Probability, Permutations, & Combinations · Permutation & Combination Permutation OR Combination 9 a. Arrangement of 10 books on a shelf b. Committee of 3 people out of a group of](https://reader034.fdocuments.in/reader034/viewer/2022050807/600b41258b4e403c6102799d/html5/thumbnails/22.jpg)
Probability
12. The table bellow lists the items in Jana’s closet.
She randomly selects 2 items. What is the probability
that she will select 2 shirts?
ItemNumber of Each Color
Black Blue White Red Purple
Shirt 2 3 1 5 5
Shoes 3 0 1 2 2
![Page 23: Probability, Permutations, & Combinations · Permutation & Combination Permutation OR Combination 9 a. Arrangement of 10 books on a shelf b. Committee of 3 people out of a group of](https://reader034.fdocuments.in/reader034/viewer/2022050807/600b41258b4e403c6102799d/html5/thumbnails/23.jpg)
Probability
13. There are 4 nickels, 3 dimes, and 5 quarters in a
purse. Find the probability.
a. P(1 dime, then 1 nickel, then another dime)
without replacement
b. P(drawing 3 coins and getting 1 of each)
![Page 24: Probability, Permutations, & Combinations · Permutation & Combination Permutation OR Combination 9 a. Arrangement of 10 books on a shelf b. Committee of 3 people out of a group of](https://reader034.fdocuments.in/reader034/viewer/2022050807/600b41258b4e403c6102799d/html5/thumbnails/24.jpg)
Homework
Worksheet 11.1