Probability
Probability
star_batch_jee_advanced_2025
Grade 12
Question:
A coin of diameter $1/2$ is tossed randomly onto the rectangular cartesian plane. The probability that the coin does not intersect any line whose equation is of the form $x = k$, or $y = k,k$ is integer, is:
Step-by-Step Solution
Key Concept: The probability equals the ratio of the favorable square's area to the total unit square's area.
For adjacent lines $x = k$ and $x = k+1$ with $y = k$ and $y = k+1$ from a unit square, the favorable event occurs when a coin falls into the shaded square of side length $\frac{1}{2}$. The desired probability is $\frac{\text{area of shaded square}}{\text{area of larger square}} = \frac{(1/2)^2}{1^2} = \frac{1}{4}$.
Correct Answer: 3