Let's break down and solve the probability questions from the image:

The problem presents three boxes (A, P, Q) containing labeled cards.

• Box A has two cards: $6$ (number) and $H$ (letter).
• Box P has four cards: $1, 8, F, K$ (two numbers, two letters).
• Box Q has five cards: $5, 9, L, M, N$ (two numbers, three letters).

For the problem:

• Step 1: A card is picked at random from Box A.
  • If the number $6$ is chosen, a card is then picked randomly from Box P.
  • If the letter $H$ is chosen, a card is picked randomly from Box Q.

We are asked to find two probabilities:

1. The probability that both cards are labeled with letters.
2. The probability that one card is labeled with a number, and the other with a letter.

(i) Probability that both cards are labeled with letters:

• Two ways to get letters:
  • If $H$ is selected from Box A, we pick from Box Q. The possible letters from Box Q are $L, M, N$ (3 letters out of 5 total cards).
  • If $6$ is selected from Box A, we pick from Box P. The possible letters from Box P are $F, K$ (2 letters out of 4 total cards).

The total probability of selecting letters in both cases is:

• Probability of picking $H$ from Box A: $\frac{1}{2}$
  • Then selecting a letter from Box Q: $\frac{3}{5}$
• Probability of picking $6$ from Box A: $\frac{1}{2}$
  • Then selecting a letter from Box P: $\frac{2}{4} = \frac{1}{2}$

Thus, the total probability is: