A and B are three mutually exclusive events . If `P(A)=0.5and P(overline(B))=0.6`,find P(A or B).

Answer

To solve the problem step by step, we will use the properties of probability and the information given in the question.

### Step 1: Understand the given information
We know that:
- \( P(A) = 0.5 \)
- \( P(\overline{B}) = 0.6 \) (where \( \overline{B} \) is the complement of event B)
- A and B are mutually exclusive events.

### Step 2: Find \( P(B) \)
Since \( P(\overline{B}) + P(B) = 1 \), we can find \( P(B) \) as follows:
\[ P(B) = 1 - P(\overline{B}) = 1 - 0.6 = 0.4 \]

### Step 3: Use the formula for mutually exclusive events
For mutually exclusive events A and B, the probability of A or B (denoted as \( P(A \cup B) \)) can be calculated using the formula:
\[ P(A \cup B) = P(A) + P(B) \]
Since \( P(A \cap B) = 0 \) for mutually exclusive events.

### Step 4: Substitute the values into the formula
Now we can substitute the values we found:
\[ P(A \cup B) = P(A) + P(B) = 0.5 + 0.4 \]

### Step 5: Calculate the final result
Now, we perform the addition:
\[ P(A \cup B) = 0.5 + 0.4 = 0.9 \]

### Final Answer
Thus, the probability of A or B is:
\[ P(A \cup B) = 0.9 \]

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