Sampling Tiles
In an earlier lesson we used data gathered by drawing tile from a bag to make predictions in an informal way. In this lesson, we'll do the same with a more focused emphasis on ranges of data, likelihood of events, and presentation of results.
For example, in drawing and replacing tiles randomly from a sack (each contains 20 tiles) of identical unknown contents, four groups might come up with this data:
They could use these displays to show their data. Then they might predict what they thought the contents of the sack would be. Which groups do you think might have created the displays below?
Which group do you think made
each prediction?
"We predict 8-10 red, 2-4 green, 7-9
blue."
"Our prediction is 14 red, 5 blue, 1 green."
"Our guess is 15 red and 5 blue"
"We think there are10 red, 9 blue, 1 green."
Here are some other tile sack contents. Do you think one of these could be the sack used in the classroom experiment?
Which is
What's the reasoning behind your decisions?
The range of experimental probabilities spans the lowest to highest probabilities for each color. After looking at each others' data, the class comes to an agreement about what the most likely contents of their sacks are. What do you think the colors of the 20 tiles in the sack are? How confident are you that the bag used in class matches your prediction? Or falls within the range of your prediction.? How does your choice of ranges affect your confidence level?
Would you like to know what the contents of the sacks used in class are? The class votes to decide whether to reveal the contents or not. What do you think? Are you confident enough in your decision to not need to look in the bag?