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JEE Main 20252 AprilEvening Shift
Exam
JEE Main
Year
2025
Date
2 April
Shift
Evening Shift
Subject
Mathematics
Chapter
Probability

JEE Main 2025 · 2 April · Evening Shift · Mathematics · Probability

Given three indentical bags each containing 10 balls, whose colours...

Given three indentical bags each containing 10 balls, whose colours are as follows :
RedBlueGreenBag I325Bag II433Bag III514\begin{array}{cccc} & \text{Red} & \text{Blue} & \text{Green} \\ \text{Bag I} & 3 & 2 & 5 \\ \text{Bag II} & 4 & 3 & 3 \\ \text{Bag III} & 5 & 1 & 4\end{array}
A person chooses a bag at random and takes out a ball. If the ball is Red, the probability that it is from bag I is p and if the balls is Green, the probability that it is from bag III is q , then the value of (1p+1q)\left(\frac{1}{\mathrm{p}}+\frac{1}{\mathrm{q}}\right) is :Given three indentical bags each containing 10 balls, whose colours are as follows : array cccc & Red & Blue & Green

Options

  1. A66
  2. B99
  3. C77
  4. D88

Correct answer

C. 77

Step-by-step solution

Given three indentical bags each containing 10 balls, whose colours are as follows : array cccc & Red & Blue & Green
\mathrm{p}=\mathrm{P}\left(\frac{\mathrm{B}_{\mathrm{I}}}{\mathrm{R}}\right)=\frac{\frac{1}{3}\left(\frac{3}{10}\right)}{\frac{1}{3}\left(\frac{3}{10}+\frac{4}{10}+\frac{5}{10}\right)}=\frac{1}{4}
q=(BIIIG)=13(410)13(510+310+410)=13∴1p+1q=7\begin{aligned} & \mathrm{q}=\left(\frac{\mathrm{B}_{\mathrm{III}}}{\mathrm{G}}\right)=\frac{\frac{1}{3}\left(\frac{4}{10}\right)}{\frac{1}{3}\left(\frac{5}{10}+\frac{3}{10}+\frac{4}{10}\right)}=\frac{1}{3} \\ & \therefore \frac{1}{\mathrm{p}}+\frac{1}{\mathrm{q}}=7\end{aligned}
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