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JEE Main20254 Apr 2025Morning ShiftMathematicsProbabilityActual

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

Options

  1. A11 15
  2. B28 75
  3. C2 15
  4. D3 5

Correct answer

B. 28 75

Step-by-step solution

array |r|c|c|c| x & x =0 & x =1 & x =2 P ( x ) & ^7 C ₂ ¹⁰ C ₂ & ^7 C ₁^3 C ₁ ¹⁰ C ₂ & ^3 ¹⁰ C ₂ array aligned & = x _ i P ( x _ i )=0+ 7 15 + 2 15 = 3 5 & Variance ( x )= P _ i ( x _ i - )^2= 28 75 aligned

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