Let A and B be independent events such that P(A)=0.6 and P(B)=0.5 find `P(A uu B)`.

Options

A. 0.24
B. 0.76
C. 0.36
D. none of these

Answer

To find the probability of the union of two independent events A and B, we can use the formula:

\[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \]

### Step 1: Identify the probabilities of A and B
We are given:
- \( P(A) = 0.6 \)
- \( P(B) = 0.5 \)

### Step 2: Calculate the probability of the intersection of A and B
Since A and B are independent events, we can calculate the probability of their intersection using the formula:

\[ P(A \cap B) = P(A) \times P(B) \]

Substituting the values we have:

\[ P(A \cap B) = 0.6 \times 0.5 = 0.3 \]

### Step 3: Substitute the values into the union formula
Now we can substitute the values into the union formula:

\[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \]

Substituting the known values:

\[ P(A \cup B) = 0.6 + 0.5 - 0.3 \]

### Step 4: Perform the calculation
Now we perform the calculation:

\[ P(A \cup B) = 1.1 - 0.3 = 0.8 \]

### Final Answer
Thus, the probability of the union of events A and B is:

\[ P(A \cup B) = 0.8 \]

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