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The problem states that events \( A \) and \( B \) are independent, with the following probabilities provided:

\[
P(A) = 0.6, \quad P(B) = 0.3
\]

For independent events, the probability of both \( A \) and \( B \) occurring (i.e., \( P(A \text{ and } B) \)) is found by multiplying their individual probabilities:

\[
P(A \text{ and } B) = P(A) \times P(B)
\]

Substituting the given values:

\[
P(A \text{ and } B) = 0.6 \times 0.3 = 0.18
\]

So, the probability that both events occur is:

\[
P(A \text{ and } B) = 0.18
\]

Would you like more details or have any further questions?

Here are 5 related questions:
1. What is the probability of \( A \text{ or } B \) occurring for independent events?
2. How does independence affect the calculation of conditional probabilities?
3. What would change if \( A \) and \( B \) were not independent?
4. Can the probability of two mutually exclusive events be calculated similarly?
5. How is the probability of the complement of \( A \text{ and } B \) determined?

**Tip:** When dealing with independent events, always remember to multiply their probabilities to find the combined outcome.

Events A and B are independent events. Find the indicated Probability: P(A) = 0.6, P(B) = 0.3, P(A and B) = ?

Learn how to calculate the probability of independent events A and B occurring together. This problem uses the multiplication rule for independent events, with P(A) = 0.6 and P(B) = 0.3. Suitable for students in Grades 9-12.

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