Since events $A$ and $B$ are independent, the probability of both $A$ and $B$ occurring together, denoted $P(A \text{ and } B)$, can be found using the formula for the intersection of two independent events:

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

Given:

• $P(A) = 0.8$
• $P(B) = 0.9$

Now, calculate:

$P(A \text{ and } B) = 0.8 \times 0.9 = 0.72$

Thus, $P(A \text{ and } B) = 0.72$.

Would you like more details or have any questions?

Here are 5 related questions:

1. What is the formula for the union of two independent events?
2. How does dependence between events affect the calculation of $P(A \text{ and } B)$?
3. If $P(A)$ and $P(B)$ were not independent, how would you calculate $P(A \text{ and } B)$?
4. What does it mean for two events to be mutually exclusive?
5. How do you calculate $P(A \text{ or } B)$ for independent events?

Tip: Independent events do not influence each other's outcomes, so their joint probability is always the product of their individual probabilities.