Question

Two cards are drawn at random from a pack of 52 cards. The probability of getting atleast a spade and an ace, is

• A. $\frac{1}{34}$
• B. $\frac{8}{221}$
• C. $\frac{1}{26}$
• D. $\frac{2}{51}$

Answer 1

Answer: (D)

$\frac{2}{51}$

Possible outcomes $n\left(S\right)={}^{52}{C}_2$

Let $E$ be an event of getting atleast a spade and an ace
$n\left(E\right)=$ Number of ways of choosing one spade out of $13$ and $1$ ace out of $4$

$={}^{13}{C}_1\times {}^4{C}_1$

$=13\times 4=52$

$\therefore P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}=\frac{52}{{}^{52}{C}_2}=\frac{2}{51}$