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JEE Main 20254 AprilMorning Shift
Exam
JEE Main
Year
2025
Date
4 April
Shift
Morning Shift
Subject
Mathematics
Chapter
Probability

JEE Main 2025 · 4 April · Morning Shift · Mathematics · Probability

A box contains 10 pens of which 3 are defective. A sample of 2 pens...

A box contains 10 pens of which 3 are defective. A sample of 2 pens is drawn at random and let XX denote the number of defective pens. Then the variance of X is

Options

  1. A1115\frac{11}{15}
  2. B2875\frac{28}{75}
  3. C215\frac{2}{15}
  4. D35\frac{3}{5}

Correct answer

B. 2875\frac{28}{75}

Step-by-step solution

\begin{array}{|r|c|c|c|}\hline x & \mathrm{x}=0 & \mathrm{x}=1 & \mathrm{x}=2 \hline \mathrm{P}(\mathrm{x}) & \frac{{ }^7 \mathrm{C}_2}{{ }^{10} \mathrm{C}_2} & \frac{{ }^7 \mathrm{C}_1^3 \mathrm{C}_1}{{ }^{10} \mathrm{C}_2} & { }^3{ }^{10} \mathrm{C}_2 \hline\end{array}
μ=ΣxiP(xi)=0+715+215=35 Variance (x)=ΣPi(xi−μ)2=2875\begin{aligned} & \mu=\Sigma \mathrm{x}_{\mathrm{i}} \mathrm{P}\left(\mathrm{x}_{\mathrm{i}}\right)=0+\frac{7}{15}+\frac{2}{15}=\frac{3}{5} \\ & \text{ Variance }(\mathrm{x})=\Sigma \mathrm{P}_{\mathrm{i}}\left(\mathrm{x}_{\mathrm{i}}-\mu\right)^2=\frac{28}{75}\end{aligned}
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