Pieces of Eight

Two of the triangles in the diagram are shaded black. What is the probability the resulting figure has at least one line of symmetry?
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Problem



A square is divided into eight congruent triangles, as shown.

Image
Pieces of Eight


Two of these triangles are selected at random and shaded black.

What is the probability that the resulting figure has at least one line of symmetry?

 

If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.