If A and B are independent events with P(A)=0.4 and P(B)=0.9, find P(A AND B).

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.

Learn how to calculate the probability of two independent events A and B, given that P(A)=0.4 and P(B)=0.9. This problem demonstrates the use of the multiplication rule for independent events. Suitable for students in Grades 9-11.

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