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Home  >>  CBSE XII  >>  Math  >>  Probability
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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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  • 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 by balaji.thirumalai

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