Problem C

Spin to Win

Esa has created a game for his math fair using two spinners. One spinner is divided into four equal sections labeled \(1,~3,~4,\) and \(5\). The other spinner is divided into five equal sections labeled \(1,~3,~5,~9,\) and \(12\).

To play the game, a player spins each spinner once and then multiplies the two numbers the spinners land on. If this product is a perfect square, the player wins. What is the probability of winning the game?

Note: A square of any integer is
called a *perfect square*. For example, the number \(25\) is a perfect square since it can be
expressed as \(5^2\) or \(5 \times 5\).

**Theme: **Data Management