Choose the correct answer from the given four options. A box cont… - Vidyadip

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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