Smaller Random Squares

Probability Level 1

A factory manufactures wooden squares of 4 square centimeters. Due to some manufacturing defect, the side length of the square varies uniformly between 1 cm1\text{ cm} and 3 cm.3\text{ cm}.

Manager Bob wants to know how frequently the squares are smaller, i.e. less than 4 cm24\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 cm21\text{ cm}^2 and 9 cm2.9\text{ cm}^2.
  2. So, the probability that the area of the next square is less than 4 cm24\text{ cm}^2 is 38.\frac{3}{8}.

Is Bob correct?

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