To determine $P(A \cap B \cap C)$, we can use the definition of conditional probability in a step-by-step process.

We know the following:

• $P(A) = 0.58$
• $P(B | A) = 0.71$
• $P(C | A \cap B) = 0.79$

The joint probability of $A \cap B \cap C$ is calculated using the product rule of probability:

$P(A \cap B \cap C) = P(A) \times P(B | A) \times P(C | A \cap B)$

Substitute the given values:

$P(A \cap B \cap C) = 0.58 \times 0.71 \times 0.79$

Let me compute this for you.The probability of $A \cap B \cap C$ (i.e., $P(A \cap B \cap C)$) is approximately $0.325$.

Would you like further details or have any other questions?

Here are 5 related questions to consider:

1. How would the result change if $P(C|A \cap B)$ were different?
2. What is the interpretation of conditional probability in real-world scenarios?
3. How can this concept be extended to more than three events?
4. What is the probability of $P(A \cap B)$?
5. How does Bayes' Theorem relate to conditional probability?

Tip: Always ensure conditional probabilities add up consistently with the base probabilities when solving problems.