let us assume the needle falls at an angle @ with the parallel lines
so the band or area it can be said to cover along 1 line= 2l|sin@| now for no intersection, this band should lie within the lines so P=2l|sin@|/2a =l|sin@|/a
now @ moves from 0 to 2 pi continuously so P=integral of(lsin@/a) from 0 to 2 pi note the mod sign
so P=4l/a
copy-pasted from prev post... this is the required set from all angles from 0 to 2 pi
so P=(4l/a)/2*pi =2l/pi*a
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Moderation Team
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