Red queens and black jacks are removed from a pack of 52 playing cards. Find the probability that the card drawn from the remaining cards is:
a black king

Answer

To solve the problem of finding the probability that the card drawn from the remaining cards is a black king after removing red queens and black jacks, we can follow these steps:

### Step 1: Identify the cards removed
In a standard deck of 52 playing cards, there are:
- 4 queens (2 red queens and 2 black queens)
- 4 jacks (2 red jacks and 2 black jacks)

Since we are removing the 2 red queens and 2 black jacks, we have removed a total of 4 cards.

### Step 2: Calculate the total number of remaining cards
Initially, there are 52 cards in total. After removing 4 cards (2 red queens and 2 black jacks), the number of remaining cards is:
\[ 52 - 4 = 48 \]

### Step 3: Identify the number of favorable outcomes
In a standard deck, there are 4 kings (2 black kings and 2 red kings). Since we have not removed any kings, the number of black kings remaining is:
\[ 2 \text{ (black kings)} \]

### Step 4: Calculate the probability
The probability of drawing a black king from the remaining cards can be calculated using the formula:
\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
Substituting the values we found:
\[ \text{Probability} = \frac{2 \text{ (black kings)}}{48 \text{ (remaining cards)}} \]
This simplifies to:
\[ \text{Probability} = \frac{2}{48} = \frac{1}{24} \]

### Final Answer
The probability that the card drawn from the remaining cards is a black king is:
\[ \frac{1}{24} \]

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