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
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: \[ \frac{\text{Area of the smaller circle}}{\text{Area of the bigger circle}} = \frac{\pi (1)^2}{\pi (2)^2} = \frac{1}{4}. \]
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