The probability that at least one of the events A and B occurs is 0.7 and they occur simultaneously with probability 0.2. Then `P(barA)+P(barB)=`

Options

A. 1.8
B. 0.6
C. 1.1
D. 0.4

Answer

To solve the problem, we need to find \( P(\bar{A}) + P(\bar{B}) \) given the probabilities of events A and B.

### Step-by-step Solution:

1. **Understand the Given Information**:
- The probability that at least one of the events A or B occurs is given as:
\[ P(A \cup B) = 0.7 \]
- The probability that both events A and B occur simultaneously is given as:
\[ P(A \cap B) = 0.2 \]

2. **Use the Formula for the Union of Two Events**:
The formula for the probability of the union of two events is:
\[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \]
Substituting the known values into this formula:
\[ 0.7 = P(A) + P(B) - 0.2 \]

3. **Rearranging the Equation**:
Rearranging the equation to find \( P(A) + P(B) \):
\[ P(A) + P(B) = 0.7 + 0.2 = 0.9 \]

4. **Finding the Complement Probabilities**:
We know that:
\[ P(\bar{A}) = 1 - P(A) \quad \text{and} \quad P(\bar{B}) = 1 - P(B) \]
Therefore:
\[ P(\bar{A}) + P(\bar{B}) = (1 - P(A)) + (1 - P(B)) = 2 - (P(A) + P(B)) \]

5. **Substituting the Value of \( P(A) + P(B) \)**:
Now substituting the value we found:
\[ P(\bar{A}) + P(\bar{B}) = 2 - 0.9 = 1.1 \]

### Final Answer:
Thus, the value of \( P(\bar{A}) + P(\bar{B}) \) is:
\[ \boxed{1.1} \]