Intersections 26781

A rectangular grid consists of two mutually perpendicular systems of parallel lines with a distance of 2. We throw a circle with a diameter of 1 on this plane. Calculate the probability that this circle:

a) overlaps one of the straight lines;
b) do any of the intersections overlap the straight line?

Correct answer:

p1 =  0.75
p2 =  0.1963

Step-by-step explanation:

a=2 D=1 S1=a2=22=4 S2=π (D/2)2=3.1416 (1/2)20.7854  S3=(aD)2=(21)2=1  p1=S1S1S3=441=43=0.75
p2=S14 4S2=44 40.7854=0.1963



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