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.