Question

A bag contains 3 white balls, 4 green balls and 5 red balls. Three balls are drawn from the bag without replacement, find the probability that the balls are all the same color.

• A. $\frac{1}{99}$
• B. $\frac{1}{22}$
• C. $\frac{1}{34}$
• D. $\frac{3}{44}$

Answer 1

Answer: (D)

$\frac{3}{44}$

Either all are whites
$P=\frac{3}{12}\times \frac{2}{11}\times \frac{1}{10}$
$=\frac{1}{220}$
Either all are red
$P=\frac{5}{12}\times \frac{4}{11}\times \frac{3}{10}$
$=\frac{1}{22}$
Either all are green
$P=\frac{4}{12}\times \frac{3}{11}\times \frac{2}{10}$
$=\frac{1}{55}$
Hence the required probability is
$=\frac{1}{220}+\frac{1}{22}+\frac{1}{55}$
$=\frac{11}{220}+\frac{4}{220}$
$=\frac{15}{220}$
$=\frac{3}{44}$.