If the probabilities 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. `gt 0.5`
B. `0.5`
C. `le 0.5`
D. 0

Explanation

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

### Step 1: Identify the given probabilities
We are given:
- Probability that A fails, \( P(A) = 0.2 \)
- Probability that B fails, \( P(B) = 0.3 \)

### Step 2: Understand the event we want to calculate
We need to find the probability that either A or B fails, which is represented as \( P(A \cup B) \).

### Step 3: Use the formula for the union of two events
The formula for the probability of the union of two events is:
\[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \]
Where \( P(A \cap B) \) is the probability that both A and B fail.

### Step 4: Analyze the information given
In this case, we do not have the value of \( P(A \cap B) \). However, we can make an assumption about the independence of events A and B. If we assume that A and B are independent, then:
\[ P(A \cap B) = P(A) \times P(B) = 0.2 \times 0.3 = 0.06 \]

### Step 5: Substitute the values into the formula
Now we can substitute the known values into the formula:
\[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \]
\[ P(A \cup B) = 0.2 + 0.3 - 0.06 = 0.44 \]

### Step 6: Conclusion
Thus, the probability that either A or B fails is \( P(A \cup B) = 0.44 \).