Final answer:
The probability of drawing a queen on the first draw and then a king on the second draw from a standard deck of cards is 1 in 221, or approximately 0.452%.
Step-by-step explanation:
The question of drawing a queen on the first draw and a king on the second draw from a standard deck of cards involves understanding the fundamental concepts of probability within combinatorial mathematics. In a standard deck, there are 4 queens and 4 kings among the 52 cards.
For the first draw, since there are 4 queens, the probability of drawing a queen is 4/52. After drawing a queen, there are 51 cards left in the deck, and assuming the queen is not replaced, there are still 4 kings among these cards. Therefore, the probability of drawing a king on the second draw is 4/51.
These probabilities must be multiplied together since we're interested in both events happening one after the other (the conjunction “and” in probability requires the product rule). So, the probability of drawing a queen first and then a king is:
(4/52) × (4/51) = 1/13 × 1/17 = 1/221.
The probability of this two-event sequence happening is therefore 1 in 221, or approximately 0.00452, or 0.452%.