A square of side n meters contains n circles of radius 1m. If the probability of hitting a circle is at least half, what is the minimum number of circles?
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Given : A square of side n meters contains n circles of radius 1m . the probability of hitting a circle is at least half
To find : maximum number of circles
Solution:
A square of side n meters
Area of square = n² m²
n circle of radius 1 m
Area = n π (1)² = nπ m²
Probability of hitting a circle = Area of circle / Total Area
= nπ / n²
= π / n
π / n > 1/2
=> n < 2π
=> n < 6.28
maximum number of circles = 6
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