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Probability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsProbability1 Mark
MCQ
Choose the correct answer from the given four options. A box contains 3 orange balls, 3 green balls and 2 blue balls. Three balls are drawn at random from the box without replacement. The probability of drawing 2 green balls and one blue ball is:
  • ✓
    $\frac{3}{28}$
  • B
    $\frac{2}{21}$
  • C
    $\frac{1}{28}$
  • D
    $\frac{167}{168}$
✓

Answer

Correct option: A.
$\frac{3}{28}$
Probability of drawing 2 green balls and one blue ball

$=\text{P}_\text{G}\cdot\text{P}_\text{G}\cdot\text{P}_\text{B}+\text{P}_\text{B}\cdot\text{P}_\text{G}\cdot\text{P}_\text{G}+\text{P}_\text{G}\cdot\text{P}_\text{B}\cdot\text{P}_\text{G}$

$=\frac{3}{8}\cdot\frac{2}{7}\cdot\frac{2}{6}+\frac{2}{8}\cdot\frac{3}{7}\cdot\frac{2}{6}+\frac{3}{8}\cdot\frac{2}{7}\cdot\frac{2}{6}$

$=\frac{1}{28}+\frac{1}{28}+\frac{1}{28}=\frac{3}{28}$

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