Question

Two cards are drawn at random from a pack of $52$ cards. The probability of these two being "Aces" is

• A. $\frac{1}{26}$
• B. $\frac{1}{221}$
• C. $\frac{1}{2}$
• D. $\frac{1}{13}$

Answer 1

The correct option is B $\frac{1}{221}$

Total Number of "Aces" in pack of card is $4$.

So, $n\left(E\right){=}^4{C}_2=6$

and $n\left(S\right){=}^{52}{C}_2=26\times 51$

Hence required probability $=\frac{n\left(E\right)}{n\left(S\right)}=\frac{6}{26\times 51}=\frac{1}{13\times 17}=\frac{1}{221}$