Task of the Week: Random pixels at the insect hotel

The task was created during the MoMaTrE project during a meeting with our partners in Nitra, Slovakia.

In a courtyard of the philosopher Konstantin-University Nitra, the atrium, there is the so-called insect hotel. The front of this object is protected by a fence and the underlying wood painted in the colors of the Slovak flag. The task is to calculate the proportion of the red color. However, the basic space consists not only of the painted surfaces, but includes the whole fence. Therefore, we decided in the task to motivate them as a random experiment.

The front side of the insect hotel is protected by a fence with the shape of little squares. These squares could be seen as pixels. One pixel is chosen randomly. Calculate the probability that the chosen pixel contains red color. Enter the result in percent.

The meshes of the fence are square and we have considered these as pixels. How big is the probability that the selected pixel contains red in the purely random choice of a pixel? To get the number of pixels, you can count them or calculate them as the compound area of ​​a rectangle and a trapezoid. Then you have to count the red pixels. The result is then the Laplace probability “favorable by possible cases” since the probability for each pixel is the same.