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JEE Main 20244 AprilMorning Shift
Exam
JEE Main
Year
2024
Date
4 April
Shift
Morning Shift
Subject
Mathematics
Chapter
Probability

JEE Main 2024 · 4 April · Morning Shift · Mathematics · Probability

Three urns A, B and C contain 7 red, 5 black; 5 red, 7 black and 6...

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\mathrm{A} is :

Options

  1. A518\frac{5}{18}
  2. B516\frac{5}{16}
  3. C417\frac{4}{17}
  4. D718\frac{7}{18}

Correct answer

A. 518\frac{5}{18}

Step-by-step solution

 A  B  C 7R,5 B5R,7 B6R,6 B\begin{array}{ccc}\text{ A } & \text{ B } & \text{ C } \\ 7 \mathrm{R}, 5 \mathrm{~B} & 5 \mathrm{R}, 7 \mathrm{~B} & 6 \mathrm{R}, 6 \mathrm{~B}\end{array}
P(B)=13⋅512+13⋅712+13⋅612 required probability =13⋅51213⋅[512+712+612]=518\begin{aligned} & \mathrm{P}(\mathrm{B})=\frac{1}{3} \cdot \frac{5}{12}+\frac{1}{3} \cdot \frac{7}{12}+\frac{1}{3} \cdot \frac{6}{12} \\ & \text{ 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}\end{aligned}
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