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# 6-D-2-1

last edited by 2 years, 7 months ago

6.D.2.1  Represent possible outcomes using a probability continuum from impossible to certain.

In a Nutshell

The probability continuum defines the range of probabilities from 0 to 1 using the terms impossible, unlikely, likely, and certain.  Events in a probability experiment that have a probability of 0 are described as impossible. Events that have a probability of 1 are described as certain. Unlikely events have probabilities between 0 and 1/2 while likely events have probabilities between 1/2 and 1. When using the probability continuum, students will use the terms from the continuum to describe the probability of an event occurring. For example, if there are no blue marbles in a bag, selecting a blue marble at random from the bag would have a probability of 0 which would be described as impossible on the probability continuum. Another term associated with the probability continuum is equally likely.  Equally likely events have an equal chance of happening.  For example, when rolling a 6-sided die, the chance of rolling a 5 is the same as rolling a 6.  Therefore, rolling a 5 on a 6-sided die and rolling a 6 on that same die are equally likely events.  However, the actual probability of rolling one of those numbers is 1/6 which would be considered unlikely on the probability continuum.  In the case that there are only two outcomes in a probability experiment like tossing a coin, it is possible to say that each outcome is equally likely and each outcome has a probability of 1/2.

## Teacher Actions

• Develop a deep and flexible conceptual understanding of the probability continuum by exploring several simple events and their likelihood of occurring.  (Ex. tossing a two-coin or rolling a 6-sided die)

• Develop mathematical reasoning as they describe the probability of an event occurring by using the probability continuum and the benchmark probabilities (0, 1/2, 1) associated with the continuum.

• Develop the ability to communicate mathematically through discussion and writing about strategies used to select a term from the probability continuum to describe the probability of an event occurring.
• Implement tasks that promote reasoning and problem solving involving the probability continuum by providing multiple simple experiments and real-world examples such as drawing a heart from a deck of cards or analyzing weather reports about the chance of rain.

• Facilitate meaningful mathematical discourse among students by encouraging them to share their reasoning and to analyze other approaches for selecting a term from the probability continuum to describe the chance that an event will occur.

## Misconceptions

• Events that have a probability of 0  are impossible.

• Unlikely events have probabilities between 0 and 1/2.

• Likely events have probabilities between 1/2 and 1.

• Events that have a probability of 1 are certain to happen.

• Events that have an equal chance of happening are called equally likely.

• For a probability experiment that has only two outcomes in which the outcomes are equally likely, the probability of each outcome is 1/2. (Ex. tossing a two-sided coin)

• Confuse unlikely with impossible and likely with certain. For example, it is not impossible to win the lottery, just unlikely.

OKMath Framework Introduction