Question

A point is selected at random from the interior of a circle. the probability that nt the selected point is mid way or is closer to the center than the boundary of the circle is

Answer 1

let the radius of the circle be R, then area of it is π R².

Now the area in which the needle will fall such that it's midway or closer to the centre than the boundary will be A CIRCLE OF RADIUS r = R/2.
its area is π r² = π R²/4.

so probability of that event,
P(E) = (favorable region) / (total region)
P(E) = (π R²/4) / (π R²)
so,
P(E) = ¼

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