A card is drawn from a shuffled deck of 52 cards, and not replaced. Then a second card is drawn. What is the probability that the second card is a king?
To give a more explained solution of this problem, there are 2 cases you have to consider:
Case 1: The first card drawn is a king
Case 2: The first card drawn is not a king
The reason there's a difference is because in Case 1 the taking of a king on the first card means there is a smaller chance of getting a king on the second card (because the originally taken card is not replaced).
To get the probability of the 2nd card being a king, we can find each individual probability for Cases 1 and 2 and add them together since each of those possibilities are disjoint; in other words, it's not possible that the first card drawn is a king and not a king at the same time.
If the first card drawn is a king, the probability of that happening is
If the first card drawn is not a king, the probability of that happening is
Adding these 2 possibilities together gives the overall probability of drawing a king on the 2nd draw: