Multilink Cubes
Introduction
In the previous lesson you learnt about the theoretical probability of something happening. However, in real life results are not always the same due to randomness. Today we shall look at the experimental probability a.k.a relative frequency of an event.
Dice
What is the probability of getting a "6" when you throw a die? What is that as a fraction? A decimal? A percentage?
When you throw it 6 times how "6s" do you expect? Now throw it 6 times and see if you get what you expect. Why/ why not?
Repeat the above throwing your die 12 times, ... 30 times, ... 60 times, times! Record your results in a table/spreadsheet (make a copy).
Plot your results on a time series (with "number of throws" on the x-axis and "number of sixes" on the y-axis).
What do you observe? Is this in line with what you expect? Why/why not?
What happens as the number of throws increase?
So what if we now do 600 throws? We don't want to throw a die 600 times! But... we can do this on a spreadsheet (you will learn more about this in the next lesson)!
Multilink Cube Experimental Probability (Results & Graphs).xlsxWhat do you observe? Is this in line with what you expect? Why/why not?
Cubes
How many ways are there for the cube to land when you throw it?
Amy says “There are four different ways that the cube can land, so the probability that it lands tilted is one-quarter.”
Do you agree with this statement? Why/why not?
If not, how can you work out what it is? (Hint: think about what you did in the last activity.)
You may wish to use this table (PRINT ME) to record your result.
You may also wish to make a copy of this spreadsheet.
Input your results in column A of the "graph" tab.
See how things change on the "Results Chart" tab as the number of throws increase.
Cube Probability.xlsxFurther Questions
From the activities above, you will hopefully now understand that:
increasing the number of experiments improves the reliability of the results.
if probabilities cannot be calculated theoretically, they need to be estimated through experimentation.
What problems might there be with this method of experimentation?
How else can we present our findings?
What other probability problems can be resolved by experimentation?
How many experiments might we need to do to get accurate results?
Further Practice
This probability spinner on mathspad can be a useful tool for further visualisation of probability, relative frequency and expectation.
For another activity to practise finding the experimental probability, try this (you will need a pin!)
Consolidate your understanding on relative frequency and experimental probability by doing the relevant skills practice on DrFrostMaths, CorbettMaths, MyiMaths and Eedi. Watch any video and/or go through any online lesson as you see fit.
Practise how to calculate the expected values here on transum.
Below are some worksheets to get you started with answers here and here:
Relative_Frequency_-_Worksheet_-_Relative_Frequency.docxExperimental probability.docx