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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