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.