Smaller Random Squares
Discrete Mathematics
Level
2
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:
- The area of the square to be manufactured next is a random quantity between \(1\text{ cm}^2\) and \(9\text{ cm}^2.\)
- So, the probability that the area of the next square is less than \(4\text{ cm}^2\) is \(\frac{3}{8}.\)
Is Bob correct?
by
Agnishom Chattopadhyay