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# 6-D-2-3

last edited by 2 years, 6 months ago

6.D.2.3  Demonstrate simple experiments in which the probabilities are known and compare the resulting relative frequencies with the known probabilities, recognizing that there may be differences between the two results

In a Nutshell

Probability is the measure of the likelihood that an event will occur in a probability experiment .  The measure of probability is what we expect to happen in theory when performing a probability experiment while relative frequency is a calculation that represents what actually happens when performing the experiment.  Relative frequency is calculated by dividing the number of times the event actually occurs by the total number of trials in the experiment.  Demonstrating simple experiments such as tossing a two-sided coin or rolling a 6-sided die will provide opportunities to compare what actually happens in real life (relative frequency) to what we expect to happen (known probabilities).  In these simple experiments, teachers should provide the known probabilities for students rather than having them calculate the probability for the experiment.  Relative frequency may often differ from the known probabilities for an event in an experiment, but as the experiment is repeated over and over the relative frequency will get closer to the calculation for the known probability.

## Teacher Actions

• Develop accurate and appropriate procedural fluency by exploring relative frequency (number of observed outcomes of event divided by number of trials) in several simple probability experiments, such as rolling an even number on a 6-sided die.

• Develop the ability to make predictions and conjectures about relative frequency while engaging in simple probability experiments in which the probability is known for a given event.

• Develop the ability to communicate mathematically through discussion and writing about how the relative frequency of an event in a probability experiment compares to the known probability for the event and why these two calculations may differ.
• Implement tasks that promote reasoning and problem solving about relative frequency and known probabilities by engaging students in simple experiments that have events with known probabilities, such as rolling a die or tossing a coin.

• Facilitate meaningful mathematical discourse through group discussion on how and why relative frequency may differ from known probabilities for simple experiments.

• Pose purposeful questions to assess and advance students’ reasoning as they compare relative frequency and known probabilities for a probability experiment.

## Misconceptions

• That the probability of an event is the measure of the chance of that event occurring.

• Relative frequency is a measure of actual outcomes divided by total number of trials in an experiment.

• That the next outcome in a probability experiment in which each outcome has an equal chance of happening is not dependent of the previous occurrences in the experiment.
• That the relative frequency of an event in a probability experiment may not always be equal to the known probability of the event in question.

• That the relative frequency of an event in a probability experiment will get closer to the known probability as more trials are performed in the experiment.

• Have difficulty understanding the difference between known probability and relative frequency.

• Believe that because an outcome has recently happened, it is more likely or less likely to happen in the next trial of an experiment.

OKMath Framework Introduction