Courses
Courses for Kids
Free study material
Free LIVE classes
More

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.

Last updated date: 22nd Mar 2023
Total views: 310.5k
Views today: 3.89k
Answer
VerifiedVerified
310.5k+ views
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.