Two cards are drawn at random in succession with replacement from a deck of 52 well-shuffled cards. Find the probability of getting both ‘Aces’.

Two cards are drawn at random in succession with replacement from a deck of 52 well-shuffled cards. Probability of getting both ‘Aces’ is

(A) $\dfrac{1}{169}$

(B) $\dfrac{2}{169}$

(D) $\dfrac{2}{13}$

(GATE 2007)

Answer: (A) $\dfrac{1}{169}$

Explanation:

Let $E_1$ and $E_2$ be the events of getting 'ace' in the first and the second drwans respectively.

Here, two cards are drawn with replacement.

Hence, the events $E_1$ and $E_2$ are independent.

Now, $P(E_1) = \dfrac{^4C_1}{^{52}C_1} = \dfrac{4}{52}$

and $P(E_2) = \dfrac{^4C_1}{^{52}C_1} = \dfrac{4}{52}$

Therefore, the required probability is

$= P(E_1) \times P(E_2)$

$= \dfrac{4}{52} \times \dfrac{4}{52}$

$= \dfrac{1}{169}$

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