Let two events A and B be such that `P(A)=L` , `P(B)=M` and `P(AuuB)=1`. Which one of the following is correct?

Options

A. `P(A|B) lt (L+M-1)/(M)`
B. `P(A|B) gt (L+M-1)/(M)`
C. `P(A|B) ge (L+M-1)/(M)`
D. `P(A|B) =(L+M-1)/(M)`

Answer

To solve the problem, we need to analyze the given information about the probabilities of events A and B.

### Step-by-Step Solution:

1. **Understanding the Given Information:**
We have:
- \( P(A) = L \)
- \( P(B) = M \)
- \( P(A \cup B) = 1 \)

2. **Using the Formula for 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, we get:
\[ 1 = L + M - P(A \cap B) \]

3. **Rearranging the Equation:**
Rearranging the equation to find \( P(A \cap B) \):
\[ P(A \cap B) = L + M - 1 \]

4. **Analyzing the Probability:**
Since probabilities cannot be negative, we must have:
\[ L + M - 1 \geq 0 \]
This implies:
\[ L + M \geq 1 \]

5. **Conclusion:**
Therefore, the correct conclusion based on the information provided is:
\[ L + M \geq 1 \]