  In the first part of this paper, we obtain symmetric formulae for the
probabilities that a plane convex body hits exactly 1, 2, 3, 4, 5 or 6
triangles of a lattice of congruent triangles in the plane. Furthermore, a very
simple formula for the expectation of the number of hit triangles is derived.
In the second part, we calculate the hitting probabilities in the cases where
the convex body is a rectangle, an ellipse and a half disc. Already known
results for a line segment (needle) follow as special cases of the rectangle
and the ellipse.
