Mathematics · Probability

JEE Main 2025 — 23 January, Morning Shift — Question 20

One die has two faces marked 1 , two faces marked 2 , one face marked 3 and one face marked 4. Another die has one face marked 1, two faces marked 2, two faces marked 3 and one face marked 4. The probability of getting the sum of numbers to be 4 or 5 , when both the dice are thrown together, is

Option A:
$\frac{1}{2}$
Correct
Option B:
$\frac{3}{5}$
Option C:
$\frac{2}{3}$
Option D:
$\frac{4}{9}$

Answer: A

Step-by-step solution

$\mathrm{a}=$ number or dice 1

$\mathrm{b}=$ number on dice 2

$(\mathrm{a}, \mathrm{b})=(1,3),(3,1),(2,2),(2,3),(3,2),(1,4),(4,1)$

Required probability

$=\frac{2}{6} \times \frac{2}{6}+\frac{1}{6} \times \frac{1}{6}+\frac{2}{6} \times \frac{2}{6}+\frac{2}{6} \times \frac{2}{6}+\frac{1}{6} \times \frac{2}{6}+\frac{2}{6} \times \frac{1}{6}+\frac{1}{6} \times \frac{1}{6}$

$=\frac{18}{36}$

$=\boxed{\frac{1}{2}}$

Answer key and solution verified before publishing.

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Exam: JEE Main 2025
Paper: 23 January, Morning Shift
Subject: Mathematics
Chapter: Probability
Topic: Problems based on P & C