Final answer:
The probability that the second card drawn is a club, given that the first card is already the 9 of clubs and has not been replaced, is 12/51, which is approximately 23.53%.
Step-by-step explanation:
To determine the probability that the second card is a club given that the first is the 9 of clubs, we start by acknowledging that the first card has already been drawn and it is the 9 of clubs. Since the first card is not replaced, the deck now has 51 cards remaining.
The total number of clubs initially in the deck is 13, but because the 9 of clubs has been drawn, there are now 12 clubs left out of the 51 cards. The probability of drawing a club as the second card, without replacement, is calculated as the number of clubs remaining divided by the total number of cards remaining.
The probability P of drawing a club as the second card is:
P = Number of remaining clubs / Total number of remaining cards = 12/51 or approximately 0.2353.
Therefore, the probability is 12/51, which simplifies to approximately 0.2353 or 23.53%.