Probability
Probability
star_batch_jee_advanced_2025
Grade 12
Question:
On a rod of length $6$ units, lengths $1, 2$ units are measured at random, the probability that no points of the measured lines will coincide is ______.
Step-by-Step Solution
Key Concept: Represent the problem geometrically using a rectangle where coordinates represent the positions of measured segments, and identify the favorable region analytically.
On a rod of length $a+b+c$, measure lengths $a, b$ from endpoints. The favorable region where no measured point coincides is a rectangle with area $c^2$ within a rectangle of total area $(a+c)(b+c)$. Therefore, the probability is $\frac{c^2}{(a+c)(b+c)}$.
Correct Answer: 0.45