Question

A bag contains $5$ red, $6$ green and $2$ black balls. Two balls are taken without replacement. Find the probability that both balls are black

• A. $\frac{2}{13}$
• B. $\frac{3}{78}$
• C. $\frac{1}{13}$
• D. $\frac{1}{78}$

Answer 1

The correct option is D $\frac{1}{78}$

$Totalnumberofballs=13$
$\text{total number of black balls=2}$
$weknowprobability=\frac{favourablecase}{totalno.ofcase}$
$probabilityof\text{drawing 2 black balls without replacement}$
$firstbla\text{ck ball can be drawn from 13 balls and second black}$
$\text{ball can be drawn from from 12 balls}$
$\text{Hence}$
$\text{p=}\frac{2}{13}\times \frac{1}{12}$
$=\frac{1}{78}$