Answer: The correct option is (b) [tex]\dfrac{2}{17}.[/tex]
Step-by-step explanation: We are give to find the probability of drawing three red cards, one at a time without replacement, from a deck of 52 cards.
In a deck of 52 cards, there are 26 red cards.
Since we are to draw three red cards without replacement from the deck, so
the probability of drawing first red card is
[tex]p_1=\dfrac{26}{52}=\dfrac{1}{2},[/tex]
the probability of drawing second red card is
[tex]p_2=\dfrac{25}{51},[/tex]
and the probability of drawing third red card is
[tex]p_3=\dfrac{24}{50}=\dfrac{12}{25}.[/tex]
Therefore, the required probability of drawing three red cards , one at a time without replacement, from a deck of 52 cards will be
[tex]P=p_1\times p_2\times p_3=\dfrac{1}{2}\times\dfrac{25}{51}\times\dfrac{12}{25}=\dfrac{2}{17}.[/tex]
Thus, the required probability is [tex]\dfrac{2}{17}.[/tex]
Option (b) is CORRECT.
