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
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.
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.
Recently Updated Pages
If ab and c are unit vectors then left ab2 right+bc2+ca2 class 12 maths JEE_Main

A rod AB of length 4 units moves horizontally when class 11 maths JEE_Main

Evaluate the value of intlimits0pi cos 3xdx A 0 B 1 class 12 maths JEE_Main

Which of the following is correct 1 nleft S cup T right class 10 maths JEE_Main

What is the area of the triangle with vertices Aleft class 11 maths JEE_Main

KCN reacts readily to give a cyanide with A Ethyl alcohol class 12 chemistry JEE_Main

Trending doubts
What was the capital of Kanishka A Mathura B Purushapura class 7 social studies CBSE

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Tropic of Cancer passes through how many states? Name them.

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

Name the Largest and the Smallest Cell in the Human Body ?
