What is the probability of drawing a king and then a queen without replacement?

The probability of drawing a king and then a queen without replacement is 4/663 or approximately 0.00603.

To understand this, let's break it down step by step. A standard deck of cards has 52 cards, consisting of 4 suits: hearts, diamonds, clubs, and spades. Each suit has 13 cards, including one king and one queen. Therefore, there are 4 kings and 4 queens in total.

When you draw the first card, the probability of it being a king is 4 out of 52, because there are 4 kings in the deck. This can be written as a fraction: 4/52, which simplifies to 1/13.

After drawing a king, you do not replace it, so there are now 51 cards left in the deck. Out of these, 4 are queens. The probability of drawing a queen now is 4 out of 51, or 4/51.

To find the combined probability of both events happening (drawing a king first and then a queen), you multiply the probabilities of each individual event. So, you multiply 1/13 by 4/51:

(1/13) * (4/51) = 4/663.

This fraction represents the probability of drawing a king first and then a queen without replacement. If you prefer a decimal, you can divide 4 by 663, which gives approximately 0.00603. This means there is a very small chance, about 0.603%, of drawing a king and then a queen in this manner.