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

$\begin{array}{1 1}25/102 \\ 25/51 \\ 1/2 \\ 1/102 \end{array}$

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## 1 Answer

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• If A and B are independant events, $P(A\cap\;B)=P(A)\;P(B)$
Given a pack of 52 cards, there are 26 black cards.
In a pack of 52 cards, there are 26 black cards. If A is the event that a black card is drawn, then P(A) = $\large \frac{26}{52} = \frac{1}{2}$
After drawing a black card, there are still 25 left in the pack. Let be be the event of drawing a black in the second draw, then P(B) = $\large \frac {25}{51}$
Since A and B are independent events, $P(A\cap\;B)=P(A)\;P(B)$.
$\Rightarrow$ $p(A\cap\;B)=P(both\;are\;black\;cards)$ = =$\large\;\frac{1}{2}\times\frac{25}{51}$ =$\large\frac{25}{102}$
answered Jun 19, 2013

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