There are four suits in a deck of 52 playing cards: hearts, diamonds, clubs, and spades. Each suit has 13 cards: A, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K. Suppose you draw two cards randomly without replacement. What is the probability that the first card is a heart and the second card is a king? (The result of directly drawing the King of Hearts on the first draw is also acceptable; therefore, this problem has two answers, and either is correct.

There are two scenarios to consider here:

Scenario 1: Drawing the King of Hearts first, then any card that is not a King. Scenario 2: Drawing any Heart that is not a King first, then drawing a King.

Let's calculate the probability for each scenario:

Scenario 1: The probability of drawing the King of Hearts first is 1 out of 52 (since there is only one King of Hearts in a deck of 52 cards). After drawing the King of Hearts, there are 51 cards left, and any of these cards can be drawn second. So, the probability of this scenario is (1/52) * (51/51) = 1/52.

Scenario 2: The probability of drawing any Heart that is not a King first is 12 out of 52 (since there are 13 Hearts in a deck and we are excluding the King of Hearts). After drawing a Heart that is not a King, there are 51 cards left, and 4 of these are Kings. So, the probability of this scenario is (12/52) * (4/51) = 48/2652 = 4/221.

The total probability is the sum of the probabilities of these two scenarios:

P = 1/52 + 4/221 = 0.0192 + 0.0181 = 0.0373 (rounded to four decimal places).

So, the probability that the first card is a heart and the second card is a king is approximately 0.0373, or 3.73%.