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JEE Main 202528 JanuaryMorning Shift
Exam
JEE Main
Year
2025
Date
28 January
Shift
Morning Shift
Subject
Mathematics
Chapter
Probability

JEE Main 2025 · 28 January · Morning Shift · Mathematics · Probability

Three defective oranges are accidently mixed with seven good ones...

Three defective oranges are accidently mixed with seven good ones and on looking at them, it is not possible to differentiate between them. Two oranges are drawn at random from the lot. If xx denote the number of defective oranges, then the variance of xx isThree defective oranges are accidently mixed with seven good ones and on looking at them, it is not possible to

Options

  1. A28/75
  2. B18/25
  3. C26/7526 / 75
  4. D14/2514 / 25

Correct answer

A. 28/75

Step-by-step solution

There are 3 bad oranges and 7 good oranges. ∴X=\therefore \quad X= number of bad oranges drawn. Three defective oranges are accidently mixed with seven good ones and on looking at them, it is not possible to
∴\therefore Variance =02⋅7C210C2+12⋅(3×710C2)+22(310C2)−(0+1⋅3×710C2+2⋅310C2)2=2875\begin{aligned} & =0^2 \cdot \frac{{ }^7 C_2}{{ }^{10} C_2}+1^2 \cdot\left(\frac{3 \times 7}{{ }^{10} C_2}\right)+2^2\left(\frac{3}{{ }^{10} C_2}\right) \\ & \quad-\left(0+1 \cdot \frac{3 \times 7}{{ }^{10} C_2}+2 \cdot \frac{3}{{ }^{10} C_2}\right)^2 \\ & =\frac{28}{75} \end{aligned}
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