Equivalent Fractions and Predicting the Nature of a Population from a Sample

1. Bag 1 contains 20 squares. Fill in the blanks.
(a) The first time we picked 10 squares:
_____ out of 10 were yellow.
What fraction of the 10 squares were yellow?_____
What fraction of the 20 squares should be yellow ?_____
What is the best scientific guess about how many of the 20 squares in the bag are
yellow based on the 10 squares we picked ?_____

(b) The second time we picked 10 squares:
_____ out of 10 were yellow.
What fraction of the 10 squares were yellow?_____
What fraction of the 20 squares should be yellow?_____
What is the best scientific guess about how many of the 20 squares in the bag are
yellow based on these 10 squares? Explain.

Will this best scientific guess necessarily be correct? Explain.

2. Bag 2 contains 30 squares. Fill in the blanks.
(a) The first time we picked 10 squares from bag 2:
_____ out of 10 were yellow.
What fraction of the 10 squares were yellow?_____
What fraction of the 30 squares should be yellow?_____
What is the best scientific guess about how many of the 30 squares in the bag are
yellow based on the 10 squares we picked ?_____

(b) The second time we picked 10 squares from bag 2:
_____out of 10 were yellow.
What fraction of the 10 squares were yellow?_____
What fraction of the 30 squares should be yellow?_____
What is the best scientific guess about how many of the 30 squares in the bag are
yellow based on these 10 squares?_____

3. Bag 3 contains 40 squares. Fill in the blanks.
(a) The first time we picked 10 squares from bag 3:
_____ out of 10 were yellow.
What fraction of the 10 squares were yellow?_____
What fraction of the 40 squares should be yellow?_____
What is the best scientific guess about how many of the 40 squares in the bag are
yellow based on the 10 squares we picked?_____

(b) The second time we picked 10 squares from bag 3:
_____ out of 10 were yellow.
What fraction of the 10 squares were yellow?_____
What fraction of the 40 squares should be yellow?_____
What is the best scientific guess about how many of the 40 squares in the bag are
yellow based on these 10 squares? _____