Tree Diagrams & Sample Spaces

Front

What is a tree diagram?

Back

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

Front

What is a sample space?

Back

A sample space is the set of all possible outcomes of a probability experiment.

Front

If a sock drawer has 3 colors of socks and you pick 2, how do you calculate the total combinations?

Back

Multiply the number of choices for the first pick by the number of choices for the second pick. For 3 colors, it's 3 x 3 = 9 combinations.

Front

How many outcomes are there when flipping a coin three times?

Back

There are 2^3 = 8 outcomes when flipping a coin three times.

Front

What is the formula for calculating combinations?

Back

The formula for combinations is C(n, r) = n! / (r!(n-r)!), where n is the total number of items, and r is the number of items to choose.

Front

What does 'order matters' mean in probability?

Back

'Order matters' means that different arrangements of the same items are considered different outcomes.

Front

If you have 2 types of shoes and 3 colors, how many combinations can you make?

Back

You can make 2 x 3 = 6 combinations of shoes and colors.

Front

What is the difference between permutations and combinations?

Back

Permutations consider the order of items, while combinations do not.

Front

How do you represent a sample space for rolling a die?

Back

The sample space for rolling a die is {1, 2, 3, 4, 5, 6}.

Front

What is the sample space for choosing a cereal from 5 options?

Back

The sample space includes all 5 options: {Honey Nut Cheerios, Cinnamon Toast Crunch, Cocoa Puffs, Reese's Puffs, Rice Chex}.