Question

Two cards are drawn at random in succession with replacement from a deck of 52 well shuffled card. What is the probability of getting both 'Aces'?

• A. $\frac{1}{169}$
• B. $\frac{2}{169}$
• C. $\frac{1}{13}$
• D. $\frac{2}{13}$

Answer 1

The correct option is A $\frac{1}{169}$

Probability of drawing an Ace card from a pack of cards
$=\frac{{}^4{C}_1}{{}^{52}{C}_1}$
Since cards are drawn 'with Replacement', both are independent events

So required probability
$=\frac{{}^4{C}_1}{{}^{52}{C}_1}\times \frac{{}^4{C}_1}{{}^{52}{C}_1}=\frac{1}{169}$