If `P(A)=0*65,P(B)=0*15,P(overline(A))+P(overline(B))=`

Options

A. `1*5`
B. `1*2`
C. `0*8`
D. none

Answer

To find \( P(\overline{A}) + P(\overline{B}) \), we can follow these steps:

### Step 1: Calculate \( P(\overline{A}) \)
The probability of the complement of event \( A \) is given by:
\[ P(\overline{A}) = 1 - P(A) \]
Given \( P(A) = 0.65 \):
\[ P(\overline{A}) = 1 - 0.65 = 0.35 \]

### Step 2: Calculate \( P(\overline{B}) \)
Similarly, the probability of the complement of event \( B \) is given by:
\[ P(\overline{B}) = 1 - P(B) \]
Given \( P(B) = 0.15 \):
\[ P(\overline{B}) = 1 - 0.15 = 0.85 \]

### Step 3: Add \( P(\overline{A}) \) and \( P(\overline{B}) \)
Now we can add the probabilities of the complements:
\[ P(\overline{A}) + P(\overline{B}) = 0.35 + 0.85 \]
Calculating this gives:
\[ P(\overline{A}) + P(\overline{B}) = 1.20 \]

### Final Answer
Thus, the final answer is:
\[ P(\overline{A}) + P(\overline{B}) = 1.20 \]

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