# Smaller Random Squares

A factory manufactures wooden squares of 4 square centimeters. Due to some manufacturing defect, the side length of the square varies uniformly between $$1\text{ cm}$$ and $$3\text{ cm}.$$

Manager Bob wants to know how frequently the squares are smaller, i.e. less than $$4\text{ cm}^2$$ in area. He made the following observations:

1. The area of the square to be manufactured next is a random quantity between $$1\text{ cm}^2$$ and $$9\text{ cm}^2.$$
2. So, the probability that the area of the next square is less than $$4\text{ cm}^2$$ is $$\frac{3}{8}.$$

Is Bob correct?

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