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To solve this problem, we need to find the probability of the complement of event \( B \), denoted as \( P(B^C) \), given that \( P(B) = 0.9 \).

In probability theory, the complement rule states:

\[
P(B^C) = 1 - P(B)
\]

Given:
\[
P(B) = 0.9
\]

Now, applying the complement rule:

\[
P(B^C) = 1 - 0.9 = 0.1
\]

So, the answer is \( P(B^C) = 0.1 \).

Would you like more details or have any questions? 

Here are 5 related questions you might find helpful:

1. What is the complement rule in probability?
2. How do you interpret probabilities in terms of real-world scenarios?
3. What is the difference between independent and mutually exclusive events?
4. How does the addition rule in probability work with complements?
5. What is conditional probability, and how is it different from the complement rule?

**Tip:** Always remember that the sum of the probability of an event and its complement is equal to 1.

Learn how to solve a basic probability problem by using the complement rule. In this example, given P(B) = 0.9, find the complement P(B^C). This step-by-step solution is suitable for high school students in Grades 9-12.

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