Let Ajay will not appear in JEE exam with probability p =2/7 , while both Ajay and Vijay will appear in the exam with probability q =1/5 . Then the probability, that Ajay will appear in the exam and Vijay will not appear is :

Mathematics · Probability

JEE Main 2024 — 1 February, Shift 2 — Question 19

Let Ajay will not appear in JEE exam with probability $\mathrm{p}=\frac{2}{7}$ , while both Ajay and Vijay will appear in the exam with probability $\mathrm{q}=\frac{1}{5}$ . Then the probability, that Ajay will appear in the exam and Vijay will not appear is :

Option A:
$\frac{9}{35}$
Option B:
$\frac{18}{35}$
Correct
Option C:
$\frac{24}{35}$
Option D:
$\frac{3}{35}$

Answer: B

Step-by-step solution

$\mathrm{P}(\overline{\mathrm{A}})=\frac{2}{7}=\mathrm{p}$

$\mathrm{P}(\mathrm{A} \cap \mathrm{V})=\frac{1}{5}=\mathrm{q}$

$\mathrm{P}(\mathrm{A})=\frac{5}{7}$

Ans. $\mathrm{P}(\mathrm{A} \cap \overline{\mathrm{V}})=\frac{18}{35}$

Answer key and solution verified before publishing.

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Exam: JEE Main 2024
Paper: 1 February, Shift 2
Subject: Mathematics
Chapter: Probability
Topic: Introduction to Probability