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If the first triangle selected to be shaded is a corner triangle, then the final figure will have at least one line of symmetry provided that the second triangle selected is one of five triangles. For example, if A is chosen first then there will be at least one line of symmetry in the final figure if the second triangle selected is B, D, E, G or H.
The same applies if an inner triangle is selected first: for example, if B is chosen first then there will be at least one line of symmetry in the final figure if the second triangle selected is A, C, F, G or H.
So, the probability that the final figure has at least one line of symmetry is $\frac{5}{7}$.
Pieces of Eight
Age 11 to 14
ShortChallenge Level 
If the first triangle selected to be shaded is a corner triangle, then the final figure will have at least one line of symmetry provided that the second triangle selected is one of five triangles. For example, if A is chosen first then there will be at least one line of symmetry in the final figure if the second triangle selected is B, D, E, G or H.
The same applies if an inner triangle is selected first: for example, if B is chosen first then there will be at least one line of symmetry in the final figure if the second triangle selected is A, C, F, G or H.
So, the probability that the final figure has at least one line of symmetry is $\frac{5}{7}$.
This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.
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