If A and B be two mutually exclusive events in a sample space such that , `P(A) = 2/5 and P(B) = 1/2 ` then
find `P (A uu B ) `:

Options

A. `7/16`
B. `9/16`
C. `9/10`
D. `1/2`

Answer

To solve the problem, we need to find the probability of the union of two mutually exclusive events A and B, given their individual probabilities.

### Step-by-Step Solution:

1. **Understand the Given Information**:
- We have two mutually exclusive events A and B.
- The probabilities are given as:
- \( P(A) = \frac{2}{5} \)
- \( P(B) = \frac{1}{2} \)

2. **Recall the Formula for the Union of Two Mutually Exclusive Events**:
- For mutually exclusive events, the probability of the union of A and B is given by:
\[ P(A \cup B) = P(A) + P(B) \]
- This is because mutually exclusive events cannot occur at the same time, so their intersection is zero.

3. **Substitute the Values into the Formula**:
- Now, substitute the values of \( P(A) \) and \( P(B) \) into the formula:
\[ P(A \cup B) = P(A) + P(B) = \frac{2}{5} + \frac{1}{2} \]

4. **Find a Common Denominator**:
- The denominators are 5 and 2. The least common multiple (LCM) of 5 and 2 is 10.
- Convert both fractions to have a denominator of 10:
- \( \frac{2}{5} = \frac{2 \times 2}{5 \times 2} = \frac{4}{10} \)
- \( \frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10} \)

5. **Add the Two Fractions**:
- Now, add the two fractions:
\[ P(A \cup B) = \frac{4}{10} + \frac{5}{10} = \frac{9}{10} \]

6. **Conclusion**:
- Therefore, the probability of the union of events A and B is:
\[ P(A \cup B) = \frac{9}{10} \]

### Final Answer:
\[ P(A \cup B) = \frac{9}{10} \]