Question

Two cards are drawn successively with replacement from a pack of $52$ cards. The probability of drawing two aces is

• A. $\frac{1}{169}$
• B. $\frac{1}{221}$
• C. $\frac{1}{2652}$
• D. $\frac{4}{663}$

Answer 1

The correct option is A

$\frac{1}{169}$

Find the required probability:

Total number of cards in a pack $=52$

Total number of aces in a pack $=4$

Let $A$ be the event of drawing an ace

$\Rightarrow$ $p\left(A\right)=\frac{4}{52}$

Now after drawing the first card as an ace we replace it in the pack again.

Hence, the pack again has $52$ cards with $4$ aces.

The probability of drawing an ace again $=\frac{4}{52}$

Both these events are independent events.

Hence, the probability of drawing two successive aces with replacement $=\frac{4}{52}\times \frac{4}{52}$

$=\frac{1}{{13}^2}$

$=\frac{1}{169}$

Hence the probability of drawing two successive aces with replacement is $\frac{1}{169}$.

Hence, option (A) is the correct answer.