#### Math - 2019-20

# 5.15 - Probability

**The
student will **

**determine**the probability of an outcome by constructing a sample space or using the Fundamental (Basic) Counting Principle.

*Adopted: 2016*

### BIG IDEAS

- So that I can use probability in sport competitions to try to figure out who is mostly likely to win
- So that a Meteorologist can predict the weather
- So that I can figure out all the different ways that I can arrange an outfit
- So that I can choose a combination of food items on a menu with many options
- So that I can win a variety of board games such as Boggle, Clue, or Scrabble

### UNDERSTANDING THE STANDARD

- A spirit of investigation and experimentation should
permeate probability instruction, where students are actively engaged in
explorations and have opportunities to use manipulatives, tables, tree
diagrams, and lists.
- Probability is the measure of likelihood that an event will
occur. An event is a collection of outcomes from an investigation or
experiment.
- The probability of an event can be expressed as a fraction,
where the numerator represents the number of favorable outcomes and the
denominator represents the total number of possible outcomes. If all the
outcomes of an event are equally likely to occur, the probability of the event is
equal to:

__number of favorable outcomes__

total number of possible outcomes.

- Probability is quantified as a number between zero and one.
An event is “impossible” if it has a probability of zero (e.g., the probability
that the month of April will have 31 days). An event is “certain” if it has a probability
of one (e.g., the probability that if today is Thursday then tomorrow will be
Friday).
- When a probability experiment has very few trials, the
results can be misleading. The more times an experiment is done, the closer the
experimental probability comes to the theoretical probability (e.g., a coin
lands heads up half of the time).
- Students should have opportunities to describe in informal
terms (i.e.,
*impossible*,*unlikely*,*equally likely*,*likely*, and*certain*) the degree of likelihood of an event occurring. Activities should include practical examples. - A sample space represents all possible outcomes of an
experiment. The sample space may be organized in a list, chart, or tree
diagram.
- Tree diagrams can be used to illustrate all possible
outcomes in a sample space. For example, how many different outfit combinations
can you make from two shirts (red and blue) and three pants (black, white,
khaki)? The sample space displayed in a tree diagram would show the outfit
combinations: red-black; red-white; red-khaki; blue-black; blue-white;
blue-khaki. Exploring the use of tree
diagrams for modeling combinations helps students develop the Fundamental
Counting Principle. For this problem,
applying the Fundamental Counting Principle shows there are 2 x 3 = 6 outcomes.
- The
Fundamental (Basic) Counting Principle is a computational procedure to
determine the total number of possible outcomes when there are multiple choices
or several events. It is the product of the number of outcomes for each choice
or event that can be chosen individually. For example, the possible final
outcomes or outfits of four shirts (green, yellow, blue, red), two shorts (tan
or black), and three shoes (sneakers, sandals, flip flops) is 4 x 2 x 3 = 24 outfits.

### ESSENTIALS

**The student will use
problem solving, mathematical communication, mathematical reasoning,
connections, and representations to**

- Construct a sample space, using a tree diagram to identify
all possible outcomes.
- Construct a sample space, using a list or chart to represent
all possible outcomes.
- Determine the probability of an outcome by constructing a
sample space. The sample space will have a total of 24 or fewer equally likely
possible outcomes.
- Determine the number of possible outcomes by using the
Fundamental (Basic) Counting Principle.

### KEY VOCABULARY

*Updated: May 29, 2019*