Two cards are drawn at random and without replacement from a pack of 52 playing cards. Finds probabi

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14.Probability

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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.

A

$\frac{25}{102}$

B

$\frac{25}{102}$

C

$\frac{25}{102}$

D

$\frac{25}{102}$

Solution

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 $=\frac{1}{2} \times \frac{25}{51}=\frac{25}{102}$

Standard 11

Mathematics

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(JEE MAIN-2013)