Mathematics · Probability

JEE Main 2025 — 23 January, Evening Shift — Question 10

A board has 16 squares as shown in the figure : Out of these 16 squares, two squares are chosen at random. The probability that they have no side in common is :

Option A:
$\frac{4}{5}$
Correct
Option B:
$\frac{7}{10}$
Option C:
$\frac{3}{5}$
Option D:
$\frac{23}{30}$

Answer: A

Step-by-step solution

Total ways for selecting any two squares $={ }^{16} \mathrm{C}_{2}$ $=120$

Total ways for selecting common side squares

$=\underbrace{3 \times 4}_{\text {Horizontal side }}+\underbrace{3 \times 4}_{\text {vertical side }}$

$=24$

so required probability

$=1-\frac{24}{120}$

$=\frac{4}{5}$

Answer key and solution verified before publishing.

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Exam: JEE Main 2025
Paper: 23 January, Evening Shift
Subject: Mathematics
Chapter: Probability
Topic: Introduction to Probability