Mathematics · Probability

JEE Main 2024 — 4 April, Shift 1 — Question 2

Three urns A, B and C contain 7 red, 5 black; 5 red, 7 black and 6 red, 6 black balls, respectively. One of the urn is selected at random and a ball is drawn from it. If the ball drawn is black, then the probability that it is drawn from urn A is :

Option A:
$\frac{4}{17}$
Option B:
$\frac{5}{18}$
Correct
Option C:
$\frac{7}{18}$
Option D:
$\frac{5}{16}$

Answer: B

Step-by-step solution

$A$	$B$	$C$
$7R,5B$	$5R,7B$	$6R,6B$

$\text{P}\left( \text{B} \right)=\frac{1}{3}\cdot \frac{5}{12}+\frac{1}{3}\cdot \frac{7}{12}+\frac{1}{3}\cdot \frac{6}{12}$

required probability $=\frac{\frac{1}{3}\cdot \frac{5}{12}}{\frac{1}{3}\cdot \left[ \frac{5}{12}+\frac{7}{12}+\frac{6}{12} \right]}=\frac{5}{18}$

Answer key and solution verified before publishing.

Practise Probability

Start with this question, then two more from the same chapter — with a tutor that explains every step. Free.

Solve a similar one free

Exam: JEE Main 2024
Paper: 4 April, Shift 1
Subject: Mathematics
Chapter: Probability
Topic: Total Probability and Baye's Theorem