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13. probability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths13. probability1 Mark
MCQ
A bag contains $8$ balls, whose colours are either white or black. $4$balls are drawn at random without replacement and it was found that $2$ balls are white and other $2$ balls are black. The probability that the bag contains equal number of white and black balls is:
  • A
     $\frac{2}{5}$
  • ✓
    $\frac{2}{7}$
  • C
    $\frac{1}{7}$
  • D
     $\frac{1}{5}$
✓

Answer

Correct option: B.
$\frac{2}{7}$
b
$ \mathrm{P}(4 \mathrm{~W} 4 \mathrm{~B} / 2 \mathrm{~W} 2 \mathrm{~B})=$

$ \frac{P(4 W 4 B) \times P(2 W 2 B / 4 W 4 B)}{P(2 W 6 B) \times P(2 W 2 B / 2 W 6 B)+P(3 W 5 B) \times P(2 W 2 B / 3 W 5 B)}  +\ldots \ldots \ldots+P(6 W 2 B) \times P(2 W 2 B / 6 W 2 B)$

$ =\frac{\frac{1}{5} \times \frac{{ }^4 \mathrm{C}_2 \times{ }^4 \mathrm{C}_2}{{ }^8 \mathrm{C}_4}}{\frac{1}{5} \times \frac{{ }^2 \mathrm{C}_2 \times{ }^6 \mathrm{C}_2}{{ }^8 \mathrm{C}_4}+\frac{1}{5} \times \frac{{ }^3 \mathrm{C}_2 \times{ }^5 \mathrm{C}_2}{{ }^8 \mathrm{C}_4}+\ldots+\frac{1}{5} \times \frac{{ }^6 \mathrm{C}_2 \times{ }^2 \mathrm{C}_2}{{ }^8 \mathrm{C}_4}}$

$ =\frac{2}{7}$

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