Two concentric circles are drawn on the plane, the radii of which are 3 cm and 5 cm. What is the probability that a point thrown at random into a large circle will fall into a ring formed by these circles?
Let’s find the areas of the small and large circle:
S = n * R² = n * 5² = 25п;
s = n * r² = n * 3² = 9п.
Then the area of the ring formed by these circles is equal to
F = S – s = 25п – 9п = 16п.
The probability that a point thrown at random into a large circle will fall into the ring is
P = F / S = 16п / 25п = 16/25 = 0.64 = 64%.
Answer: P = 0.64, or P = 64%.
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