Tio Mané has two boxes, one with seven distinct balls numbered from 1 to 7 and another with eight distinct balls numbered with all prime numbers less than 20. He draws one ball from each box.

Suggestion: Calculate the probability of the product being odd. What is the probability that the product of the numbers on the balls drawn is even?
The product of the numbers drawn is odd only if both balls drawn have odd numbers.

The probability of drawing an odd-numbered ball from the first box is $4 / 7$ and the probability of drawing an odd-numbered ball from the second box is $7 / 8$, because this box contains balls with the numbers $\{2,3,5,7,11,13,17,19\}$.

Thus, the probability that the product of the numbers from the boxes is odd

$$
\frac{4}{7} \times \frac{7}{8}=\frac{1}{2}
$$

Therefore, the probability that the product is even is $1-1 / 2=1 / 2$.