Answer: The correct option is (C) [tex]\dfrac{1}{221}.[/tex]
Step-by-step explanation: Given that two cards are drawn from a standard 52-card deck without replacement.
We are to find the probability that both the cards are aces.
We know that there are 4 aces in a deck of 52 cards.
Let S denote the sample space for the experiment of drawing a card from a deck of 52 cards.
Then, n(S) = 52.
Let A denote the event that the first card drawn is an ace.
Then, n(A) = 4.
So, probability of event A will be
[tex]P(A)=\dfrac{n(A)}{n(S)}=\dfrac{4}{52}=\dfrac{1}{13}.[/tex]
Now, since the second card is drawn without replacing the first ace card, so the probability that both the cards are aces will be
[tex]P=P(A)\times \dfrac{3}{51}=\dfrac{1}{13}\times\dfrac{3}{51}=\dfrac{1}{221}.[/tex]
Thus, the required probability is [tex]\dfrac{1}{221}.[/tex]
Option (C) is CORRECT.
