If `A and B` are two events and `P(A) = 0.3 , P(B) = 0.4 , P(A cap B) = 0.5` then `P(A cup B)` =

Options

A. `0.5`
B. `0.2
C. 1
D. `0.1`

Answer

To find the probability of the union of two events \( A \) and \( B \), we can use the formula:

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

Given:
- \( P(A) = 0.3 \)
- \( P(B) = 0.4 \)
- \( P(A \cap B) = 0.5 \)

Now, we can substitute these values into the formula:

1. **Substituting the values:**
\[ P(A \cup B) = 0.3 + 0.4 - 0.5 \]

2. **Calculating the sum of \( P(A) \) and \( P(B) \):**
\[ 0.3 + 0.4 = 0.7 \]

3. **Subtracting \( P(A \cap B) \):**
\[ 0.7 - 0.5 = 0.2 \]

Thus, the probability of the union of events \( A \) and \( B \) is:

\[ P(A \cup B) = 0.2 \]

### Final Answer:
\[ P(A \cup B) = 0.2 \]