Probability
Probability
star_batch_jee_advanced_2025
Grade 12
Question:
A point is selected at random inside a circle. The probability that the point is closer to the centre of the circle than to its circumference :
Step-by-Step Solution
Key Concept: Geometric probability reduces to the ratio of areas when the condition defines a region within the sample space.
For the favorable case, points must lie inside the concentric circle of radius $\frac{r}{2}$. The desired probability is the ratio of the area of the smaller circle to the area of the larger circle: $\frac{\pi(r/2)^2}{\pi r^2} = \frac{1}{4}$.
Correct Answer: 3