# 4.13 - Probability

The student will

a)  determine the likelihood of an outcome of a simple event;

b)  represent probability as a number between 0 and 1, inclusive; and

c)  create a model or practical problem to represent a given probability.

### BIG IDEAS

• So that I can predict the outcome of a sporting event based on given data

• So that I can predict the likelihood of teams moving on to the next level during March Madness

• A Meteorologist uses probability when predicting the weather.  Meteorologists report the probability of rain, snow, thunderstorms etc.

### 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.
• Probability is the measure of likelihood that an event will occur. An event is a collection of outcomes from an investigation or experiment.
• The terms certain, likely, equally likely, unlikely, and impossible can be used to describe the likelihood of an event.  If all outcomes of an event are equally likely, 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 0 and 1.  An event is “impossible”if it has a probability of 0 (e.g., if eight balls are in a bag, four yellow and four blue, there is zero probability that a red ball could be selected).  An event is “certain”if it has a probability of one (e.g., the probability that if 10 coins, all pennies, are in a bag that it is certain a penny could be selected).
• For an event such as flipping a coin, the things that can happen are called outcomes.  For example, there are two possible outcomes when flipping a coin: the coin can land heads up, or the coin can land tails up.  The two possible outcomes, heads up or tails up, are equally likely.
• For another event such as spinning a spinner that is one-third red and two-thirds blue, the two outcomes, red and blue, are not equally likely. This is an unfair spinner (since it is not divided equally), therefore, the outcomes are not equally likely.

• Equally likely events can be represented with fractions of equivalent value.  For example, on a spinner with eight sections of equal size, where three of the sections are labeled G (green) and three are labeled B (blue), the chances of landing on green or on blue are equally likely; the probability of each of these events is the same, or 3/8.
• Students need opportunities to create a model or practical problem that represents a given probability. For example, if asked to create a box of marbles where the probability of selecting a black marble is 4/8, sample responses might include:

• 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).

### ESSENTIALS

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

• Model and determine all possible outcomes of a given simple event where there are no more than 24 possible outcomes, using a variety of manipulatives (e.g., coins, number cubes, and spinners). (a)
• Determine the outcome of an event that is least likely to occur or most likely to occur where there are no more than 24 possible outcomes. (a)
• Write the probability of a given simple event as a fraction, where there are no more than 24 possible outcomes. (b)
• Determine the likelihood of an event occurring and relate it to its whole number or fractional representation (e.g., impossible or zero; equally likely; certain or one). (a, b)
• Create a model or practical problem to represent a given probability. (c)

### KEY VOCABULARY

Updated: Aug 22, 2018