Question

Two cards are drawn successively without replacement from a well-shuffled pack of $52$ cards. The probability of drawing two aces is.

• A. $1/26$
• B. $1/221$
• C. $4/223$
• D. $1/13$

Answer 1

The correct option is B $1/221$

Deck contains $52$ cards out of which $4$ are aces.

Let $A$ denotes the event that first ace is drawn.

Let $B$ denotes the event that second ace is drawn.

$P\left(A\right)=\frac{{}_1^{4}C}{{}_1^{52}C}=\frac{4}{52}=\frac{1}{13}$

$P\left(\frac{B}{A}\right)=\frac{{}_1^{3}C}{{}_1^{51}C}=\frac{3}{51}=\frac{1}{17}$

The required probability $=\frac{1}{13}\times \frac{1}{17}=\frac{1}{221}$