To solve this, we need to recall the formula for the complement of an event:

$P(E') = 1 - P(E)$

Here, $P(E) = 99.6\%$, or $0.996$ in decimal form.

Now calculate $P(E')$:

$P(E') = 1 - 0.996 = 0.004$

Convert $P(E')$ back to percentage form:

$P(E') = 0.004 \times 100 = 0.4\%$

Final Answer:

$P(E') = 0.4\%$

Would you like additional details or explanations? Here are some related questions to deepen your understanding:

1. What is the relationship between an event and its complement in probability?
2. How do you ensure that probabilities always sum to 1?
3. Can an event and its complement occur simultaneously?
4. What are practical examples of complements in probability scenarios?
5. How is this concept applied in real-world decision-making?

Tip: Always double-check that the sum of $P(E)$ and $P(E')$ equals 100% for consistency.