Question

A flashlight has $8$ batteries out of which $3$ are dead. If two batteries are selected without replacement and tested, the probability that both are dead is

Answer 1

$\text{Total number of batteries}=8$
Among them $3$ are dead
Let, $E_1=\text{The event that, the first selected battery is dead}$
and, $E_2=\text{The event that, the second selected battery is dead}$
The required probability is
$P\left(\text{Both the battery is dead}\right)$
$=P(E_1\cap E_2)$
$=P\left(E_1\right)\times P\left(E_2/E_1\right)$
$=\frac{3}{8}\times \frac{2}{7}$
$=\frac{3}{28}$
Hence, the correct option is (d).