The problem states:

"52 cards are drawn at random. Find the chance that 1 is a King and 1 is a Queen."

Solution:

1. Understand the problem:

   • There is a standard deck of 52 cards.
   • We want to find the probability that, when 2 cards are drawn, one is a King and the other is a Queen.

2. Count the relevant cards:

   • Number of Kings in a deck = 4 (one for each suit).
   • Number of Queens in a deck = 4 (one for each suit).

3. Calculate the probability:

   • Total number of ways to draw 2 cards from 52:
     $\text{Total ways} = \binom{52}{2} = \frac{52 \times 51}{2} = 1326$
   • Number of ways to select 1 King out of 4 and 1 Queen out of 4:
     $\text{Ways to choose 1 King} = \binom{4}{1} = 4$ $\text{Ways to choose 1 Queen} = \binom{4}{1} = 4$ $\text{Total favorable outcomes} = 4 \times 4 = 16$

4. Find the probability: $\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{16}{1326} \approx 0.0121$

   Thus, the probability that one of the drawn cards is a King and the other is a Queen is approximately 0.0121 or 1.21%.

Would you like a more detailed explanation or have any questions?

Here are some related questions for further practice:

1. What is the probability of drawing two aces from a standard deck of cards?
2. If three cards are drawn, what is the chance that one is a King, one is a Queen, and one is an Ace?
3. What is the probability of drawing two consecutive cards that are both face cards (Jack, Queen, King)?
4. What is the probability of drawing two cards of the same suit from a deck of 52 cards?
5. How many ways can you draw three cards such that one is a King and the others are not?

Tip: Remember, when calculating probabilities, always divide the number of favorable outcomes by the total number of possible outcomes.