Unit 2 Vocab-Advanced Counting

A _______ is a visual representation used to show all possible outcomes of a sequence of events. It uses branches to display choices step-by-step so you can systematically count outcomes without missing any.

• tree diagram

• bar graph

• pie chart

• line plot

The Fundamental Counting Principle (FCP) states that if one event can happen in m ways and a second event can happen in n ways, then the two events together can happen in ______ ways (assuming each choice is independent).

• m x n

• m + n

• m - n

• m / n

The explicit formula for an arithmetic sequence is _______.

• a_n = a_1 + (n - 1)d

• a_n = a_1 + nd

• a_n = a_1 - (n - 1)d

What is a recursive pattern?

• A recursive pattern defines each term using the term before it.

• A recursive pattern defines each term using random values.

• A recursive pattern defines each term using the sum of all previous terms.

• A recursive pattern defines each term without any relation to previous terms.

In a tree diagram, what are branches?

• Branches are the lines that represent possible choices or outcomes at each stage of an event.

• Branches are the labels given to each node in the diagram.

• Branches are the points where two lines intersect in the diagram.

• Branches are the shaded regions representing probabilities in the diagram.

What is the formula for permutations where order matters? Example: Arranging 3 books on a shelf in different orders.

• nPr = n! / (n - r)!

• nPr = n! / r!

• nPr = n! * r!

• nPr = (n - r)! / n!

Which of the following describes mutually exclusive (disjoint) events? Two events are mutually exclusive (disjoint) if they cannot happen at the same time. If one occurs, the other cannot. Example: Rolling a 2 and rolling a 5 on the same single die roll.

• Both events can happen at the same time.

• If one occurs, the other cannot.

• Both events must occur together.

A node is a point on a tree diagram where branches begin or end. It represents a ______ or outcome in the counting process.

• stage

• leaf

• root

• branch

The sample size is the total number of possible ______. Example: Flipping a coin 3 times has a sample size of 8 outcomes.

• outcomes

• choices

• events

• results

The Pigeonhole Principle states that if you have more objects than containers, at least one container must hold more than one ______. Example: If 13 people are in a room, at least two people must share the same birth month.

• object

• container

• person

• month