(i) The probability that Fabio chooses Americano and leaves it to drink later is given by the product of the probability of choosing Americano and the probability of leaving it to drink later. This is calculated as:

\(P(A \text{ Later}) = 0.5 \times 0.2 = 0.1\)

(ii) To find the probability that Fabio chose Latte given that he drinks his coffee immediately, we use Bayes' theorem. Let \(L\) be the event that he chooses Latte, and \(I\) be the event that he drinks immediately. We need to find \(P(L \mid I)\).

First, calculate \(P(I)\), the total probability of drinking immediately:

\(P(I) = (0.5 \times 0.8) + (0.3 \times 0.6) + (0.2 \times 0.1) = 0.4 + 0.18 + 0.02 = 0.6\)

Now, calculate \(P(L \cap I)\), the probability that he chooses Latte and drinks immediately:

\(P(L \cap I) = 0.2 \times 0.1 = 0.02\)

Finally, apply Bayes' theorem:

\(P(L \mid I) = \frac{P(L \cap I)}{P(I)} = \frac{0.02}{0.6} = 0.0333\)