Two cards are dealt at random from a standard deck of 52 cards. What is the probability that the first card is a King and the second card is a Heart?
There are 4 kings in a deck of cards, and 13 hearts in a deck of cards. So, the answer is 4/52*13/51, if there are no replacements.
Probability that the first card is a king of spades, clubs or diamonds, followed by a heart is p1 = 3/52*13/51
Probability that the first card is the king of hearts, followed by a heart is p2 = 1/52*12/51
Total probability = p1 + p2 = (3*13 + 1*12)/(52*51) = 51/(52*51) → 1/52