Two cards are drawn at random and without replacement from a pack of $52$ playing cards. Finds the probability that both the cards are black.
Two cards are drawn at random and without replacement from a pack of $52$ playing cards. Finds the probability that both the cards are black.
There are $26$ black cards in a deck of $52$ cards.
Let $P(A)$ be the probability of getting a black card in the first draw.
$\therefore $ $P(A)=\frac{26}{52}=\frac{1}{2}$
Let $\mathrm{P}(\mathrm{B})$ be the probability of getting a black card on second draw. since the card is not replaced,
$\therefore $ $P(B)=\frac{25}{51}$
Thus, probability of getting both the cards black $=\frac{1}{2} \times \frac{25}{51}=\frac{25}{102}$
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- [IIT 1988]