Use the given information to find the indicated probability.
A ∩ B = ∅, P(A) = 0.2, P(A ∪ B) = 0.3. Find P(B).
P(B) =

Given that \( A \cap B = \emptyset \) (which means \( A \) and \( B \) are mutually exclusive events), we have the following information:

- \( P(A) = 0.2 \)
- \( P(A \cup B) = 0.3 \)

We want to find \( P(B) \).

Since \( A \) and \( B \) are mutually exclusive, we can use the formula:

\[
P(A \cup B) = P(A) + P(B)
\]

Substitute the given values:

\[
0.3 = 0.2 + P(B)
\]

Solving for \( P(B) \):

\[
P(B) = 0.3 - 0.2 = 0.1
\]

Therefore:

\[
P(B) = 0.1
\]

Would you like further details or have any questions about this problem?

Here are 5 related questions to expand your understanding:

1. If \( P(A) = 0.4 \) and \( P(A \cup B) = 0.6 \), and \( A \cap B = \emptyset \), what is \( P(B) \)?
2. How would the solution change if \( A \) and \( B \) were not mutually exclusive?
3. Can you find \( P(A \cup B) \) if \( P(A) = 0.25 \) and \( P(B) = 0.15 \), assuming \( A \cap B = \emptyset \)?
4. What does it mean for two events to be mutually exclusive, and how does that affect their probabilities?
5. How can you determine whether two events are independent given their probabilities?

**Tip:** When dealing with mutually exclusive events, remember that the intersection of such events is always zero. This simplifies the calculation of union probabilities.

Use the given information to find the indicated probability. A ∩ B = ∅, P(A) = 0.2, P(A ∪ B) = 0.3. Find P(B).

Solve the probability problem where P(A) = 0.2, P(A ∪ B) = 0.3, and A ∩ B = ∅. Learn how to calculate P(B) using the formula for mutually exclusive events. Suitable for students in Grades 10-12.

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