If $A$ and $B$ are independent events, the probability of both $A$ and $B$ happening together, denoted as $P(A \text{ AND } B)$, is given by the product of their individual probabilities:

$P(A \text{ AND } B) = P(A) \times P(B)$

Given that:

$P(A) = 0.4 \quad \text{and} \quad P(B) = 0.9,$

we can calculate:

$P(A \text{ AND } B) = 0.4 \times 0.9 = 0.36.$

Thus, $P(A \text{ AND } B) = 0.36$.

Would you like more details or have any further questions?

Here are 5 related questions:

1. What is the probability of $A$ or $B$ happening, i.e., $P(A \text{ OR } B)$?
2. How do you calculate the probability of $A$ given that $B$ has occurred?
3. If $P(A) = 0.4$ and $P(B) = 0.9$, what is the probability of neither $A$ nor $B$ happening?
4. What would happen to the probability if $A$ and $B$ were mutually exclusive instead of independent?
5. Can two events be independent and mutually exclusive at the same time? Why or why not?

Tip: Independence means that knowing the outcome of one event does not affect the probability of the other event occurring.