How to find the probability that a point is at a distance less than r from the center?

Z

zhanna_vaganova2015-10-23 19:50:39

Mathematics

zhanna_vaganova, 2015-10-23 19:50:39

A point is thrown at random inside a circle of radius R. The probability of the point falling into any area located inside the circle is proportional to the area of this area. Find the probability that a point is at a distance less than r from the center ( r < R )

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2 answer(s)

M

ManWithBear, 2015-10-24
@zhanna_vaganova

Probability r^2 / R^2

M

Mrrl, 2015-10-23
@Mrl

1. Find the area of the region containing all points located at a distance less than r from the center
2. Understand the probability that the point will fall into a circle of radius R
3. Find the area of a circle of radius R
4. Use the fact that probabilities are proportional to areas .
I'm just wondering which of these points can be problematic at all.