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The problem you're working on involves finding the probability \( P(A \cap B \cap C) \), where \( A \), \( B \), and \( C \) are independent events, given:

- \( P(A) = 0.1 \)
- \( P(B) = 0.6 \)
- \( P(C) = 0.9 \)

Since \( A \), \( B \), and \( C \) are independent events, the probability of all three occurring simultaneously (the intersection \( P(A \cap B \cap C) \)) is simply the product of the individual probabilities:

\[
P(A \cap B \cap C) = P(A) \times P(B) \times P(C)
\]

Now, let's calculate this.

\[
P(A \cap B \cap C) = 0.1 \times 0.6 \times 0.9
\]

I'll compute this for you.The probability of \( A \), \( B \), and \( C \) all occurring together, \( P(A \cap B \cap C) \), is \( 0.054 \).

Would you like a detailed explanation of this process, or do you have any further questions?

Here are 5 related questions:
1. How do you find the probability of the union of independent events?
2. What happens if events \( A \), \( B \), and \( C \) are not independent?
3. Can you explain the difference between independent and mutually exclusive events?
4. How do you calculate the conditional probability \( P(A \mid B) \)?
5. What is the formula for calculating \( P(A \cup B) \)?

**Tip:** When events are independent, their joint probability is simply the product of their individual probabilities.

Let A, B, and C be independent events with P(A) = 0.1, P(B) = 0.6, and P(C) = 0.9. Find P(A ∩ B ∩ C).

Learn how to calculate the probability of the intersection of independent events with P(A) = 0.1, P(B) = 0.6, and P(C) = 0.9. Using the multiplication rule for independent events, the solution is P(A ∩ B ∩ C) = 0.054.

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