Abstract
In this paper we consider the two events that a random congruent copy of a convex body meets each one of two given families of equidistant lines in the plane. The probabilities are easily calculated. Then it is discovered that there always exists a value for the angle α between the nonparallel lines, such that the two events be independent. For convex bodies of constant width, and only for them, the two events are independent for any α.
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