From a pack of regular playing cards, two cards are drawn at random. What is the probability that both cards will be kings if the card is NOT replaced?

(A) $\dfrac{1}{26}$

(B) $\dfrac{1}{52}$

(D) $\dfrac{1}{221}$

Answer: (D) $\dfrac{1}{221}$

Explanation:

Let $E_1$ and $E_2$ be the events of getting the first king and the second king respectively.

Here, two cards are drawn without replacement. In this case, the probabilities for the second pick are affected by the result of the first pick.

Now, the probability of getting the first king is

$= P(E_1) = \dfrac{4}{52}$

and the probability of getting the second king is

$P(E_2) = \dfrac{3}{51}$

Therefore, the required probability is

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

$= \dfrac{4}{52} \times \dfrac{3}{51}$

$= \dfrac{1}{221}$

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