Question

A coin is thrown at random into the red triangle below.

A triangle with red outline.

What is the likelihood that the coin will fall into a blue region of the red triangle?
It is certain.
It is impossible.
It is likely.
It is unlikely.

Answer 1

I can’t see the diagram you mention. Could you upload the image or describe how the blue regions are arranged inside the red triangle (e.g. number of small triangles, positions, are they congruent, are they formed by drawing medians/parallel lines/inscribed shapes, etc.)?

How I’ll solve it once I have the picture:
- The probability = (area of blue regions) / (area of the whole red triangle).
- Choose a convenient side length for the big triangle, compute its area, compute the total area of the blue parts (by symmetry, subtraction, or decomposing into known shapes), then form the ratio and simplify.
If you upload the image I’ll compute the exact likelihood and choose the correct wording (certain / impossible / likely / unlikely).