Two cards are drawn at random and without replacement from a puck of 52 playing cards. Find the probability that both the cards are black.

.: Let ${E_1}$ be the event when first drawn card is black card.

$\Rightarrow P\left( {{E_1}} \right) = 26/52 = 1/2$

Let ${E_2}$ be the event when second drawn card is black without replacement,

then
$P\left( {{E_2}/{E_1}} \right) = 25/51$

Hence, the required probability is

$P\left( {{E_1} \cap {E_2}} \right) = P\left( {{E_1}} \right)P\left( {{E_2}/{E_1}} \right) = \cfrac{{26}}{{52}} \times \cfrac{{25}}{{51}} = \cfrac{{25}}{{102}}$