Fundamental Counting Principle

The Fundamental Counting Principle allows you to...

• see each and every possible outcome possibility in your sample.

• find the number of total outcomes in your sample.

• count how many times you must do a tree diagram.

• see how many outcomes will not show up on a tree diagram.

Use the Fundamental Counting Principle to find out how many total outcomes you have:

You are buying a car and have to make the following decisions: (brand: Toyota, Honda, Ford), (color: Red, Green, Blue, Black, Silver), (transmission: Manual or Automatic)

• 10

• 3

• 30

• 72

Tags

CCSS.HSS.CP.B.9

Use the Fundamental Counting Principle to find out how many total outcomes you have:

You go to an ice cream shop and get to choose: (flavor: Chocolate, Vanilla, Strawberry, Swirl), (scoops: 1, 2, or 3), (toppings: Sprinkles, Gummi Bears, Nerds, Chocolate Chips), and (cone: Waffle or Sugar).

• 96

• 4

• 14

• 240

Tags

CCSS.HSS.CP.B.8

Use the Fundamental Counting Principle to find out how many total outcomes you have:

You go to an entertainment center and get to pick how to spend the day with friends: (activity 1: go-karts, bowling, mini golf), (food: hot dogs, corn dogs, hamburgers, pizza), and (activity 2: laser tag, arcade, skating)

• 80

• 10

• 3

• 36

Tags

CCSS.HSS.CP.B.8

CCSS.HSS.CP.B.9

Use the Fundamental Counting Principle to find out how many total outcomes you have:

You toss 4 coins: (coin 1: H or T), (coin 2 : H or T), (coin 3 (H or T), and (coin 4: H or T)

• 8

• 81

• 16

• 4

Use the Fundamental Counting Principle to find out how many total outcomes you have:

You roll 2 dice and flip 3 coins: (die 1: 1, 2, 3, 4, 5, 6), (die 2: 1, 2, 3, 4, 5, 6), (coin 1: H or T), (coin 2: H or T), and (coin 3: H or T)

• 18

• 288

• 392

• 5

Tags

CCSS.HSS.CP.B.8

You are buying a car and have to make the following decisions: (brand: Toyota, Honda, Ford), (color: Red, Green, Blue, Black, Silver), (transmission: Manual or Automatic).

What is the probability of buying a Toyota (brand) in Blue or Red (color) with Manual drive (transmission)? (Hint: You can still use the Fundamental Counting Principle to find your numerator (what you want to buy) and then your denominator (your original choices.)

•  $\frac{4}{30}=\frac{2}{15}$  

•  $\frac{3}{30}=\frac{1}{10}$  

•  $\frac{2}{30}=\frac{1}{15}$  

•  $\frac{1}{30}$  

Tags

CCSS.HSS.CP.B.9

You roll 2 dice and flip 3 coins: (die 1: 1, 2, 3, 4, 5, 6), (die 2: 1, 2, 3, 4, 5, 6), (coin 1: H or T), (coin 2: H or T), and (coin 3: H or T).

What is the probability of rolling an EVEN number on the first die, an ODD number on the second die, and all HEADS for the three coins? (Hint: You can still use the Fundamental Counting Principle to find your numerator (what you want to buy) and then your denominator (your original choices.)

•  $\frac{1}{288}$  

•  $\frac{9}{18}=\frac{1}{2}$  

•  $\frac{9}{392}$  

•  $\frac{9}{288}=\frac{1}{32}$  

Tags

CCSS.HSS.CP.B.9

You go to an entertainment center and get to pick how to spend the day with friends: (activity 1: go-karts, bowling, mini golf), (food: hot dogs, corn dogs, hamburgers, pizza), and (activity 2: laser tag, arcade, skating). 

What is the probability of selecting to go-kart, eat ANY of the four food options, and ending the day with laser tag? (Hint: You can still use the Fundamental Counting Principle to find your numerator (what you want to buy) and then your denominator (your original choices.)

• $\frac{6}{36}=\frac{1}{6}$

• $\frac{4}{80}=\frac{1}{20}$

• $\frac{4}{36}=\frac{1}{9}$

• $\frac{4}{13}$

Tags

CCSS.HSS.CP.B.9

You go to an ice cream shop and get to choose: (flavor: Chocolate, Vanilla, Strawberry, Swirl), (scoops: 1, 2, or 3), (toppings: Sprinkles, Gummi Bears, Nerds, Chocolate Chips), and (cone: Waffle or Sugar). 

What is the probability of buying a Swirl, Two-scoop ice cream with Chocolate Chips on a Waffle Cone? (Hint: You can still use the Fundamental Counting Principle to find your numerator (what you want to buy) and then your denominator (your original choices.)

•  $\frac{4}{96}=\ \frac{1}{24}$ 

• $\frac{4}{16}=\frac{1}{4}$

• $\frac{4}{4}=1$

•  $\frac{1}{96}$ 

Tags

CCSS.HSS.CP.B.9