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.