Question

Two cards are drawn one after the other without replacement from a well shuffuled pack of 52 cards. The probability of drawing a face card on first draw and and an ace on the second is $\frac{A}{B}$, then the value of $A+B$ is

• A. 225

Answer 1

The correct option is A 225
$P\left(\text{Face card on first draw}\right)=\frac{12}{52}=\frac{3}{13}$

Now there are $51$ cards in pack of cards as 1 card is already drawn without replacement
$P\left(\text{An ace on second draw}\right)=\frac{4}{51}$

$P\left(\text{Required Probability}\right)=\frac{3}{13}\times \frac{4}{51}=\frac{4}{221}$

$\therefore \frac{A}{B}=\frac{4}{221}$

Hence, $A+B=4+221=225$