### Instruction: Two cards are chosen at random from a standard 52-card deck.  What is the probability that the first card is a heart and the second card is a 10?### Response: To find the probability of two events happening in sequence, I need to multiply the probabilities of each event separately, as long as they are independent.
However, in this case, the events are not independent, because the outcome of the first card affects the number of cards left in the deck for the second draw.
So I need to adjust the probabilities accordingly.
The probability of the first card being a heart is 13/52, since there are 13 hearts in the deck and 52 cards total.
The probability of the second card being a 10 depends on whether the first card was a 10 or not.
If the first card was a 10, then there are only 3 10s left in the deck, out of 51 cards.
If the first card was not a 10, then there are still 4 10s left in the deck, out of 51 cards.
So I need to account for both scenarios and add their probabilities.
The probability of the first card being a 10 of hearts and the second card being any 10 is (1/52) * (3/51), since there is only one 10 of hearts in the deck.
The probability of the first card being any other heart and the second card being any 10 is (12/52) * (4/51), since there are 12 other hearts in the deck and 4 10s.
Adding these two probabilities, I get (1/52) * (3/51) + (12/52) * (4/51) = (3/2652) + (48/2652) = 51/2652.
This can be simplified by dividing both the numerator and the denominator by 3, giving me 17/884.
This is the final answer.