**Given the following information, answer questions a - d.**
P(A)=0.51
P(B)=0.55
A and B are independent.
*Round all answers to 5 decimal places as needed*
**Find P(A∩B)**

Given that events \(A\) and \(B\) are independent, the probability of both events happening (the intersection \(P(A \cap B)\)) can be found using the formula for independent events:

\[
P(A \cap B) = P(A) \times P(B)
\]

### Given:
- \(P(A) = 0.51\)
- \(P(B) = 0.55\)

Now, compute \(P(A \cap B)\):

\[
P(A \cap B) = 0.51 \times 0.55 = 0.2805
\]

Thus, the probability \(P(A \cap B)\) is:

\[
P(A \cap B) = 0.28050
\]

### Final answer:  
\[
P(A \cap B) = 0.28050
\]

Would you like further details or have any questions?

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Here are 5 related questions:
1. What is the probability of \(P(A \cup B)\)?
2. How does independence affect the calculation of \(P(A \cap B)\)?
3. If \(P(A \cap B) = 0.1\), what is the relationship between \(A\) and \(B\)?
4. What happens if \(A\) and \(B\) are mutually exclusive instead of independent?
5. How would \(P(A \mid B)\) change if \(A\) and \(B\) were dependent?

**Tip:** Always verify whether events are independent or dependent before applying probability rules.

Given the following information, answer questions a - d. P(A)=0.51, P(B)=0.55, A and B are independent. Round all answers to 5 decimal places as needed. Find P(A∩B).

Learn how to calculate the probability of the intersection of two independent events, A and B, with given probabilities P(A) = 0.51 and P(B) = 0.55. Using the formula for independent events, we compute P(A ∩ B) = 0.28050, rounding to 5 decimal places. Suitable for high school students in Grades 9-12.

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