Question

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?

Answer 1

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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