Data Sufficiency

If a point is to be selected at random from the set of all possible points in a rectangle with an area of 30, what is the probability that the point lies inside or on a circle of radius R ?

(1) R = 2

(2) The center of the circle is inside the rectangle.

Answer is E. But I would like to know how you would have solved this problem if this was a PS...

Something like:
If a point is chosen at random from the set of all possible point in a rectangle, what is the probability that point lies inside or on a circle of radius R when the radius of the circle is 2 and the center of a circle is inside the circle and circle is fully inscribed inside the rectangle...

I have attached figure for this PS question...
The DS problem was from a Kaplan test...

I would like to know how you would have solved this problem if this was a PS...

Something like:
If a point is chosen at random from the set of all possible point in a rectangle, what is the probability that point lies inside or on a circle of radius R when the radius of the circle is 2 and the center of a circle is inside the circle and circle is fully inscribed inside the rectangle...

Req prob = favourable outcome/total outcome
= area of circle lies within rectangle/Area of rectangle

akdayal wrote:

I would like to know how you would have solved this problem if this was a PS...

Something like:
If a point is chosen at random from the set of all possible point in a rectangle, what is the probability that point lies inside or on a circle of radius R when the radius of the circle is 2 and the center of a circle is inside the circle and circle is fully inscribed inside the rectangle...

Req prob = favourable outcome/total outcome
= area of circle lies within rectangle/Area of rectangle

So that would be 4Pi/30 = 2Pi/15?
Pls conform!!

@adi_800
Yes, you are right as in question mentioned that circle is fully inscribed inside the rectangle