**Given the following information, answer questions a - d.**
P(A)=0.55
P(B)=0.54
A and B are independent.
*Round all answers to 5 decimal places as needed*
**Find P(A∣B)**

Since events \(A\) and \(B\) are independent, the probability of \(A\) given \(B\) is equal to the probability of \(A\). This is because, in independent events, knowing that \(B\) has occurred does not change the likelihood of \(A\) occurring.

So, for independent events:

\[
P(A \mid B) = P(A)
\]

Given that \( P(A) = 0.55 \), we conclude:

\[
P(A \mid B) = 0.55
\]

Would you like more details or have any other questions on this?

Here are 5 related questions to consider:
1. How would you find \( P(B \mid A) \)?
2. What is the formula for the probability of the intersection of two independent events?
3. How do you calculate \( P(A \cup B) \) for independent events?
4. If \( P(A \cap B) = P(A) \times P(B) \), what is the intersection probability here?
5. What changes if events \(A\) and \(B\) are dependent instead of independent?

**Tip:** Independence implies that the occurrence of one event does not affect the probability of the other event.

Given the following information, answer questions a - d.
P(A)=0.55
P(B)=0.54
A and B are independent.
*Round all answers to 5 decimal places as needed*
Find P(A∣B).

Explore how to calculate P(A ∣ B) when events A and B are independent. Learn key concepts of probability theory, including conditional probability and the formula for independent events. This problem demonstrates how P(A ∣ B) equals P(A) due to event independence. Suitable for students in Grades 10-12.

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