Given that`P(A)=0.5, P(B)=0.35, P(AuuB)=0.7` find `P(AnnB)`.

Answer

To find \( P(A \cap B) \) given \( P(A) = 0.5 \), \( P(B) = 0.35 \), and \( P(A \cup B) = 0.7 \), we can use the formula for the probability of the union of two events:

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

### Step-by-Step Solution:

1. **Write down the formula for the union of two events:**
\[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \]

2. **Substitute the known values into the formula:**
\[ 0.7 = 0.5 + 0.35 - P(A \cap B) \]

3. **Calculate \( 0.5 + 0.35 \):**
\[ 0.5 + 0.35 = 0.85 \]
So, the equation now looks like:
\[ 0.7 = 0.85 - P(A \cap B) \]

4. **Rearrange the equation to solve for \( P(A \cap B) \):**
\[ P(A \cap B) = 0.85 - 0.7 \]

5. **Perform the subtraction:**
\[ P(A \cap B) = 0.15 \]

### Final Answer:
\[ P(A \cap B) = 0.15 \]