Final answer:
The probability that the first card was a heart and the second was a diamond given that the third card was an ace is 132/2550.
Step-by-step explanation:
To determine the probability that the first card was a heart and the second was a diamond given that the third card was an ace, we need to consider the total number of possible outcomes and the number of favorable outcomes. Since the third card is an ace, there are now 51 cards left in the deck, of which 12 are hearts and 11 are diamonds. The probability of drawing a heart on the first card is 12/51, and the probability of drawing a diamond on the second card is 11/50. To find the probability of both events happening, we multiply these two probabilities together: (12/51) x (11/50) = 132/2550. Therefore, the probability that the first card was a heart and the second was a diamond given that the third card was an ace is 132/2550.