A deck of 52 cards is shuffled, and you draw two cards one after the other without replacement. What is the probability of drawing a queen first and then a king?

To calculate the probability of drawing a queen first and then a king, let's break it down into steps:

### Step 1: Probability of drawing a queen first
There are 4 queens in a standard deck of 52 cards. So, the probability of drawing a queen first is:

\[
P(\text{Queen first}) = \frac{4}{52} = \frac{1}{13}
\]

### Step 2: Probability of drawing a king second (without replacement)
After drawing a queen, there are only 51 cards left in the deck, and 4 of those cards are kings. So, the probability of drawing a king after drawing a queen is:

\[
P(\text{King second | Queen first}) = \frac{4}{51}
\]

### Step 3: Total probability of drawing a queen first and then a king
Since these two events (drawing a queen and drawing a king) are dependent, we multiply their probabilities:

\[
P(\text{Queen first and King second}) = P(\text{Queen first}) \times P(\text{King second | Queen first}) = \frac{1}{13} \times \frac{4}{51} = \frac{4}{663}
\]

Thus, the probability of drawing a queen first and then a king is:

\[
\boxed{\frac{4}{663}}
\]

Would you like more details or have any questions?

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Here are 5 related questions you might find interesting:
1. What is the probability of drawing two kings in a row?
2. What is the probability of drawing a queen and then another queen?
3. How does the probability change if the cards are drawn with replacement?
4. What is the probability of drawing a face card first and then an ace?
5. How does the calculation change if three cards are drawn instead of two?

**Tip:** When solving probability problems with multiple steps, always consider whether the events are independent or dependent.

Discover how to calculate the probability of drawing a queen first and then a king from a shuffled deck of 52 cards, step-by-step. This problem covers essential probability concepts, including dependent events and the multiplication rule, suitable for Grades 9-11.

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