Question

From a pack of $52$ cards, two cards are drawn together at random. What is the probability of both the cards being kings ?

• A. $\frac{1}{15}$
• B. $\frac{25}{57}$
• C. $\frac{35}{256}$
• D. $\frac{1}{221}$

Answer 1

Answer: (D)

$\frac{1}{221}$

Let S be the sample space Then
n(S)=${}^{52}{C}_2=\frac{(52\times 51)}{(2\times 1)}=1326$
Let E= event of getting 2 kings out of 4
$\therefore n\left(E\right){=}^4{C}_2=\frac{(4\times 3)}{(2\times 1)}=6$
$\therefore P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}=\frac{6}{1326}=\frac{1}{221}$