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alex7449
11.02.2020 •
Mathematics
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.
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Ответ:
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%)
Ответ: