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The question asks for the probability of picking one red card followed by one black card from a standard deck of playing cards, without replacement.

### Step-by-Step Solution:
1. **Deck Composition**:
   - A standard deck has 52 cards.
   - There are 26 red cards (hearts and diamonds).
   - There are 26 black cards (spades and clubs).

2. **First Draw (Red Card)**:
   The probability of drawing a red card on the first draw is:
   \[
   P(\text{Red}) = \frac{26}{52} = \frac{1}{2}
   \]

3. **Second Draw (Black Card, Without Replacement)**:
   After drawing a red card, only 51 cards remain, and 26 of them are black. The probability of drawing a black card after removing one red card is:
   \[
   P(\text{Black | Red}) = \frac{26}{51}
   \]

4. **Total Probability**:
   The probability of both events happening (red first, then black) is the product of the two probabilities:
   \[
   P(\text{Red and Black}) = P(\text{Red}) \times P(\text{Black | Red}) = \frac{1}{2} \times \frac{26}{51} = \frac{26}{102} = \frac{13}{51}
   \]

Thus, the correct answer is **\(\frac{13}{51}\)**.

Let me know if you'd like further details on any part of the explanation!

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Here are 5 related questions:
1. What is the probability of drawing two red cards in succession, without replacement?
2. What is the probability of drawing one black card followed by one red card, without replacement?
3. How would the probability change if the cards were drawn with replacement?
4. What is the probability of drawing one red card and one black card in any order, without replacement?
5. How many total possible outcomes are there when drawing two cards from a deck, without replacement?

**Tip**: When calculating probabilities involving multiple events, multiply the individual probabilities of each event happening sequentially.

With a standard deck of playing cards, what is the probability of picking one red card followed by one black card, without replacement?

Learn how to calculate the probability of drawing a red card followed by a black card from a standard deck of 52 playing cards, without replacement. This problem covers dependent events, the multiplication rule of probability, and basic combinatorics. Suitable for students in Grades 9-12.

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