Tree Diagrams & Fundamental Counting Principle Flashcard

Front

What is a tree diagram?

Back

A tree diagram is a visual representation that shows all possible outcomes of a sequence of events, branching out from a starting point.

Front

What is the Fundamental Counting Principle?

Back

The Fundamental Counting Principle states that if one event can occur in 'm' ways and a second event can occur independently in 'n' ways, then the two events can occur in 'm × n' ways.

Front

How many styles of sneakers can Jared choose if he has 2 types, 2 fastenings, and 3 colors?

Back

12 styles (2 types × 2 fastenings × 3 colors = 12).

Front

If you roll a die (6 sides) and flip a coin (2 sides), how many possible outcomes are there?

Back

12 outcomes (6 sides of the die × 2 sides of the coin = 12).

Front

What is the probability of rolling an even number on a die?

Back

The probability is 3/6 or 1/2, since there are 3 even numbers (2, 4, 6) out of 6 possible outcomes.

Front

What is the probability of flipping a head on a coin?

Back

The probability is 1/2, since there are 2 possible outcomes (heads or tails).

Front

What is the combined probability of rolling an even number and flipping a head?

Back

The combined probability is 3/12 or 1/4 (3 even numbers × 1 head = 3 favorable outcomes out of 12 total outcomes).

Front

How do you calculate the total number of outcomes in a multi-step experiment?

Back

Multiply the number of outcomes for each step together.

Front

What is the total number of outcomes when rolling a die and flipping a coin?

Back

12 outcomes (6 outcomes from the die × 2 outcomes from the coin = 12).

Front

If a pizza has 8 different toppings, how many combinations of 2 toppings can you choose?

Back

28 combinations (using the combination formula C(n, k) = n! / [k!(n-k)!], where n=8 and k=2).