Probability Fundamental Counting Theory

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

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.)

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.)

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.)

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.)

How do you do the Fundamental Counting Principle?

• You multiply the categories by 2.

• You add all the categories together.

• You add the number of options in each category.

• You multiply the number of options in each category.

Find the total number of outcomes for picking a day of the week and a month of the year.

• 19

• 84

• 60

• 210

Bag A contains 9 red marbles and 3 green marbles. Bag B contains 9 black marbles and 6 orange marbles. Find the probability of selecting one green marble from bag A and one black marble from bag B.  P(green, black)

• 3/20

• 1/4

• 3/31

• 2/27

A coin is tossed and then the spinner is spun. Determine the probability that you toss Heads and spin a Red.

• 1/6

• 1/10

• 0

• 1/12

You flip a coin and roll a die. What is the probability, in a fraction, you flip a heads and roll a 3?

• 1/6

• Bad Potato

•  1/12

• 12/1