Two cards are drawn without replacement from a standard deck of 52 playing cards. What is the probability of choosing a red card for the second card drawn, if the first card, drawn without replacement, was a diamond? Express your answer as a fraction or a decimal number rounded to four decimal places.

Answer: [tex]\dfrac{3}{51}[/tex]Step-by-step explanation:Given : The total number of cards in a deck = 52Number of red cards = 26There are two types of red  cards : diamond and heart.Number of diamond cards = 13The probability that the first card is a diamond :-[tex]\dfrac{13}{52}=\dfrac{1}{4}[/tex]Since diamond is also a red card.Now, the total cards left = 51The number of red cards left = 12The probability that the second card is a red card (without repetition) is given by :-[tex]\dfrac{12}{51}[/tex]Now, the probability of choosing a red card for the second card drawn, if the first card, drawn without replacement, was a diamond :-[tex]\dfrac{1}{4}\times\dfrac{12}{51}=\dfrac{3}{51}[/tex]