Question

Pick a uniformly chosen random point inside a unit square (a square of sidelength 1) and draw a circle of radius 1/3 around the point. Find the probability that the circle lies entirely inside the square.

Answer 1

Answer:

the probability is 4/9 (44,44%)

Step-by-step explanation:

Assuming that each point inside the square is equally probable, then the probability is uniformly distributed in area of the square. Thus

probability = area where condition is true / total area of the square

for a circle of radius 1/3  inside the square ,the area where this condition is satisfied is a square with sides 1-1/3 = 2/3 , thus

probability = (2/3)²/1² = 4/9

thus the probability is 4/9 (44,44%)