fundamental counting principle and tree diagrams

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 do you calculate the total number of outfits with multiple clothing items?

Back

Multiply the number of options for each clothing item. For example, if you have 5 pairs of jeans, 8 t-shirts, and 2 pairs of shoes, the total outfits = 5 × 8 × 2 = 80.

Front

What is a tree diagram?

Back

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

Front

What is the sample space in probability?

Back

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

Front

How many outcomes are there when flipping two coins?

Back

There are 4 outcomes: HH (both heads), HT (first head, second tail), TH (first tail, second head), TT (both tails).

Front

What is the probability of an event?

Back

The probability of an event is a measure of the likelihood that the event will occur, calculated as the number of favorable outcomes divided by the total number of possible outcomes.

Front

If a die is rolled, what are the possible outcomes?

Back

The possible outcomes when rolling a die are 1, 2, 3, 4, 5, and 6.

Front

What is the probability of rolling a number less than 6 on a die?

Back

The probability is 5/6, since the favorable outcomes are 1, 2, 3, 4, and 5.

Front

How do you find the probability of multiple independent events?

Back

Multiply the probabilities of each independent event. For example, P(A and B) = P(A) × P(B).

Front

What is the formula for calculating the number of ways to answer a test with multiple questions?

Back

If each question has 'n' choices and there are 'k' questions, the total ways to answer is n^k.