Answer: The correct option is (A) [tex]\dfrac{1}{425}.[/tex]
Step-by-step explanation: We are given to consider an example of a deck of 52 cards.
We are to find the probability of drawing three queens from a standard deck of cards, given that the first card drawn was a queen and the cards are not replaced.
We know that there are 4 queens in a deck of 52 cards.
Since the first card is already a queen and the cards are not not being replaced, so we have 3 options for 2nd queen and 2 options for 3rd queen.
That is, the total number of options for three queens is given by
[tex]n=3\times2=6.[/tex]
Now, after drawing first queen, 51 cards left in the deck and after drawing second queen, 50 cards left in the deck.
So, the probability of drawing three queens from a standard deck of cards, given that the first card drawn was a queen is
[tex]P=\dfrac{n}{51\times50}=\dfrac{6}{2550}=\dfrac{1}{425}.[/tex]
Thus, the required probability is [tex]\dfrac{1}{425}.[/tex]
Option (A) is correct.
