# 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.

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Hint: Probability of an event is the product of probabilities of its sub events.

There are 26 cards in a deck of 52 cards.

Let $P\left( A \right)$ be the probability of getting a black card in the first draw.

$\therefore P\left( A \right) = \dfrac{{26}}{{52}} = \dfrac{1}{2}$

Let $P\left( B \right)$ be the probability of getting a lack card in the second draw.

Since, the card is not replaced

Then, $P\left( B \right) = \dfrac{{25}}{{51}}$

Thus probability of getting both cards black is

$

= P\left( A \right) \times P\left( B \right) \\

= \dfrac{1}{2} \times \dfrac{{25}}{{51}} = \dfrac{{25}}{{102}} \\

= 0.2451 \\

$

Note:This problem of probability can also be solved by using the concept of combination, but this method is quite easier when lower no of selection is made. Probability of an event is the product of probabilities of its sub events when both of the events are necessary for the completion of the event.

There are 26 cards in a deck of 52 cards.

Let $P\left( A \right)$ be the probability of getting a black card in the first draw.

$\therefore P\left( A \right) = \dfrac{{26}}{{52}} = \dfrac{1}{2}$

Let $P\left( B \right)$ be the probability of getting a lack card in the second draw.

Since, the card is not replaced

Then, $P\left( B \right) = \dfrac{{25}}{{51}}$

Thus probability of getting both cards black is

$

= P\left( A \right) \times P\left( B \right) \\

= \dfrac{1}{2} \times \dfrac{{25}}{{51}} = \dfrac{{25}}{{102}} \\

= 0.2451 \\

$

Note:This problem of probability can also be solved by using the concept of combination, but this method is quite easier when lower no of selection is made. Probability of an event is the product of probabilities of its sub events when both of the events are necessary for the completion of the event.

Last updated date: 28th Sep 2023

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