If A and B are independent events such that P(A) = 0.3 and P(B) = 0 . 4 then `P(bar(A) cup bar(B))` =

Options

A. `0 . 88`
B. `0 . 52`
C. `0 . 2 `
D. `(1)/(3)`

Answer

To solve the problem, we need to find \( P(\bar{A} \cup \bar{B}) \) given that \( P(A) = 0.3 \) and \( P(B) = 0.4 \).

### Step-by-Step Solution:

1. **Understand the Complement Rule**:
We know that the probability of the union of the complements of two events can be expressed as:
\[ P(\bar{A} \cup \bar{B}) = 1 - P(A \cap B) \]

2. **Calculate \( P(A \cap B) \)**:
Since A and B are independent events, we can calculate the probability of their intersection as:
\[ P(A \cap B) = P(A) \cdot P(B) \]
Substituting the given values:
\[ P(A \cap B) = 0.3 \cdot 0.4 = 0.12 \]

3. **Substitute into the Complement Formula**:
Now we can substitute \( P(A \cap B) \) back into the formula for \( P(\bar{A} \cup \bar{B}) \):
\[ P(\bar{A} \cup \bar{B}) = 1 - P(A \cap B) = 1 - 0.12 \]

4. **Calculate the Final Probability**:
\[ P(\bar{A} \cup \bar{B}) = 1 - 0.12 = 0.88 \]

Thus, the final answer is:
\[ P(\bar{A} \cup \bar{B}) = 0.88 \]