There are two circles in xy −plane whose equations are \(x^2+y^2-2y=0\) and \(x^2+y^2-2y-3=0\). A point \((x,y)\) is chosen at random inside the larger circle. Then the probability that the point has been taken from smaller circle is
Step-by-step Solution:
Both circles have the same center \( (0, 0) \), with radii 1 and 2. It is given that a point lies within the larger circle. The probability that the point has been chosen from the smaller circle is: \[ \frac{\text{Area of the smaller circle}}{\text{Area of the bigger circle}} = \frac{\pi (1)^2}{\pi (2)^2} = \frac{1}{4}. \]