If the probability for A to fail in an examination is `0.2` and that for B is 0,3 , then the probability that either A or B fails is

Options

A. `0.5`
B. `0.06`
C. `0.56`
D. `0.44`

Answer

To solve the problem of finding the probability that either A or B fails in the examination, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the probabilities**:
- The probability that A fails, \( P(A) = 0.2 \)
- The probability that B fails, \( P(B) = 0.3 \)

2. **Use the formula for the probability of either A or B failing**:
The formula for the probability of either A or B failing (denoted as \( P(A \cup B) \)) is given by:
\[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \]
Here, \( P(A \cap B) \) is the probability that both A and B fail.

3. **Calculate \( P(A \cap B) \)**:
Since A and B are independent events, the probability that both A and B fail is:
\[ P(A \cap B) = P(A) \times P(B) = 0.2 \times 0.3 = 0.06 \]

4. **Substitute the values into the formula**:
Now we can substitute the values into the formula:
\[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \]
\[ P(A \cup B) = 0.2 + 0.3 - 0.06 \]

5. **Calculate the final probability**:
\[ P(A \cup B) = 0.5 - 0.06 = 0.44 \]

### Final Answer:
The probability that either A or B fails is \( 0.44 \).