OUTCOME PERCENTAGES

FINDING THE PERCENTAGE OF LIKELIHOOD THAT A CERTAIN OUTCOME WILL OCCUR

LET’S THINK ABOUT THIS…You are about to switch out your books from your locker during passing period but forget the order of your locker combination. You know that there are the numbers, , and in some order. What is the percent of locker combinations that start with ?Locker Combination Possibilities:

3, 16, 21, ,,,,,,,,,

How many possible combinations are there in total?

How many combinations start with 3?

What fraction represents the number of combinations that start with 3?

6

2

𝟐𝟔

or 𝟑𝟑𝟏𝟑%

All of the -letter passwords that can be formed using the letters A and B are as follows:

AAA, AAB, ABA, ABB, BAA, BAB, BBA, BBB.

What percent of passwords contain at least two B’s? 8

4

48=12

.50 50%

How many passwords are there in total?

How many passwords have at least two B’s?

What’s the fraction that represents passwords with at least two B’s?

Now we can go from a fraction to a percent:

All of the -letter passwords that can be formed using the letters A and B are as follows:

AAA, AAB, ABA, ABB, BAA, BAB, BBA, BBB.

What percent of passwords contain no A’s?

.125 12.5%

What’s the fraction that represents passwords with no A’s?

18

Now we can go from a fraction to a percent:

SHORTCUT: GOING STRAIGHT FROM A FRACTION TO A PERCENT

We can plug the fraction into our proportion:

e.g. x = 60

OR

We can multiply the fraction by 100 and it give us our percentage.Percent = Fraction x 100

e.g.

Using three different keys on a piano, a songwriter makes the beginning of his melody with three notes, C, E, and G:

CCE, EEE, EGC, GCE, CEG, GEE, CGE, GGE, EGG, EGE, GCG, EEC, ECC, ECG, GGG, GEC, CCG, CEE, CCC, GEG, CGC

From the list above, what is the percent of melodies with all three notes that are different?

From the list above, what is the percent of melodies that have three of the same notes?

𝟔𝟐𝟏

𝒙𝟏𝟎𝟎

x 100

STEPS FOR FINDING THE PERCENTAGE OF POSSIBLE

OUTCOMES1.Determine the total possible outcomes 2.Determine how many outcomes have the result you’re looking for

(favorable outcomes)3.Create a fraction4.Turn the fraction into a percentage (or plug into the )

OR

1. Determine the total possible outcomes

2. Determine how many outcomes have the result you’re looking for

(favorable outcomes)

3. Plug those numbers into: = (as 𝐐𝐮𝐚𝐧𝐭𝐢𝐭𝐲 𝐏𝐞𝐫𝐜𝐞𝐧𝐭decimal) × 𝐖𝐡𝐨𝐥𝐞• where the quantity is the number of different favorable outcomes

• the whole is the total number of possible outcomes

Peeta is baking and has 5 different ingredients: flour, milk, eggs, sugar, and chocolate chips. His cookbook has 20 recipes that use those 5 ingredients, but only 20% of those recipes use chocolate chips. How many recipes use chocolate chips?

x = (.20)20

x = 4

4 recipes use chocolate chips.

Quantity = Percent(as a decimal) x Whole

Quantity: XPercent: (as a decimal) Whole: 20

0.2

OutcomesYou have three shirts and four pairs of pants to choose from. How many different combinations are there?

5 ice cream flavors x 4 toppings= 2020 different ways to

order a sundae at Scott’s Sundae

Shop.

You Try:You order an ice cream sundae at Scott’s Sundae Shop. You have 5 ice cream flavors and 4 toppings to choose from. How many different ways could you order a sundae?

PRACTICE!