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**Problem Context:**
We have 3 boxes (A, P, and Q) with cards in each:

- **Box A** contains 2 cards: [6, H]
- **Box P** contains 4 cards: [1, 8, F, K]
- **Box Q** contains 5 cards: [5, 9, L, M, N]

The procedure described is:
- A card is picked at random from **Box A**.
- If the number card (6) is picked, another card is picked from **Box P**.
- If the letter card (H) is picked, another card is picked from **Box Q**.

We are asked to find the probability for two specific cases by listing all possible outcomes:

### (i) **Probability that both cards are labeled with letters.**

**Outcome for Box A:**
- If 6 is chosen, you pick from Box P, which could give either a letter or number.
- If H is chosen, you pick from Box Q, which could also give either a letter or number.

The favorable outcomes are:
- H from Box A and any letter from Box Q (L, M, N): (H, L), (H, M), (H, N)
- 6 from Box A and any letter from Box P (F, K): (6, F), (6, K)

Thus, possible outcomes for both cards being letters are:
- H from Box A, and one of L, M, N from Box Q.
So, favorable outcomes: (H, L), (H, M), (H, N).

Thus, there are 3 favorable outcomes for this case.

### (ii) **Probability that one card is labeled with a number and the other is labeled with a letter.**

Here, you need to find combinations where:
- A number card and a letter card are chosen.
  
Possible favorable outcomes:
- 6 from Box A, then F or K from Box P: (6, F), (6, K)
- H from Box A, then 5, 9 from Box Q: (H, 5), (H, 9)

Thus, favorable outcomes: (6, F), (6, K), (H, 5), (H, 9).

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Would you like further clarification, or do you need the final probabilities calculated?

A card is picked at random from Box A. If the number card 6 is chosen, then another card is picked at random from Box P. If the letter card H is chosen, then another card is picked at random from Box Q. The probabilities need to be found for two cases: (i) both cards are labeled with letters, and (ii) one card is labeled with a number and another with a letter.

Learn how to calculate the probability of picking a number or letter card from different boxes. This problem involves concepts of probability and combinatorics, making it suitable for high school students in Grades 10-12.

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