The probabilities that A and b can solve a problem independently are `1/3` and `1/4` respectively. If both try to solve the problem independently, find the probability that:
(i) problem will be solved

Explanation

To solve the problem, we need to find the probability that at least one of A or B solves the problem. We can denote the probabilities as follows:

- Let \( P(A) \) be the probability that A solves the problem, which is \( \frac{1}{3} \).
- Let \( P(B) \) be the probability that B solves the problem, which is \( \frac{1}{4} \).

### Step 1: Understand the problem
We need to find the probability that the problem is solved, which can be expressed as:
\[ P(A \cup B) \]
This represents the probability that either A solves the problem, or B solves the problem, or both.

### Step 2: Use the formula for the union of two events
The formula for the probability of the union of two independent events is:
\[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \]

### Step 3: Calculate \( P(A \cap B) \)
Since A and B are independent, we can calculate \( P(A \cap B) \) as:
\[ P(A \cap B) = P(A) \times P(B) \]
Substituting the values:
\[ P(A \cap B) = \frac{1}{3} \times \frac{1}{4} = \frac{1}{12} \]

### Step 4: Substitute values into the union formula
Now we can substitute \( P(A) \), \( P(B) \), and \( P(A \cap B) \) into the union formula:
\[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \]
\[ P(A \cup B) = \frac{1}{3} + \frac{1}{4} - \frac{1}{12} \]

### Step 5: Find a common denominator
To add these fractions, we need a common denominator. The least common multiple (LCM) of 3, 4, and 12 is 12. We can rewrite the fractions:
- \( \frac{1}{3} = \frac{4}{12} \)
- \( \frac{1}{4} = \frac{3}{12} \)

Now substituting these values:
\[ P(A \cup B) = \frac{4}{12} + \frac{3}{12} - \frac{1}{12} \]

### Step 6: Perform the addition and subtraction
Now we can perform the arithmetic:
\[ P(A \cup B) = \frac{4 + 3 - 1}{12} = \frac{6}{12} \]

### Step 7: Simplify the fraction
Finally, we simplify \( \frac{6}{12} \):
\[ P(A \cup B) = \frac{1}{2} \]

### Final Answer
The probability that the problem will be solved is \( \frac{1}{2} \).

---