5.3 Probability from relative frequency

To demonstrate that relative frequency is probability and to show that sample values can only lead to conclusions about what the population values are not, not what they are, a mix of two colors of marbles were used. 

Spring 2025 35 blue and 15 green marbles were put into a cloth bag. 14 students were present at the time of the draw, each blindly drew a single marble. The result was 11 blue and 3 three green for a 79% and 21% relative frequency. The actual relative frequencies were 70% and 30%. 

Fall 2024 a mix of 40 blue and 12 orange marbles was used, 77% and 23%. The draw by 21 students was 13 blue and 8 orange, 62% and 38%.  

Fall 2025 30 blue, 20 orange, and ten white marbles were placed into a cloth bag. 18 students each selected a single marble. 

Some of the questions posed ahead of the marble tally included:

What percentage of the marbles in the bag are blue, white, and orange?

Can I know the number of marbles in the bag from the sample data?

If I know the number of marbles in the bag, can I estimate how many are blue, orange and white based on the sample data?

Follow-on explanations included considerations of the minimum reasonable sample size.

An explanation was also given that while the sample probabilities will almost always be wrong, by shifting to a range around that number, the actual population probability can be captured within that range. An advanced organizer was my guessing a students age, getting that wrong, expanding the range, getting that wrong, and after expanding the rage yet again I captured their age. By shifting from a single value to a range, the population value can be captured. 

Although not show to the class, the 95% confidence intervals all captured the population probabilities.