Let's analyze the question from the image.

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).

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