A problem on mathematics is given to three students whose chances of solving it are 1/2, 1/3 and 1/4, respectively, find the probability that the problem will be solved.

Answer

To solve the problem, we need to find the probability that at least one of the three students will solve the mathematics problem. The chances of each student solving the problem are given as follows:

- Student A: Probability of solving = \( P(A) = \frac{1}{2} \)
- Student B: Probability of solving = \( P(B) = \frac{1}{3} \)
- Student C: Probability of solving = \( P(C) = \frac{1}{4} \)

### Step 1: Calculate the Probability of Each Student Not Solving the Problem
We first need to find the probability of each student not solving the problem.

- Probability that Student A does not solve the problem:
\[ P(\text{not } A) = 1 - P(A) = 1 - \frac{1}{2} = \frac{1}{2} \]

- Probability that Student B does not solve the problem:
\[ P(\text{not } B) = 1 - P(B) = 1 - \frac{1}{3} = \frac{2}{3} \]

- Probability that Student C does not solve the problem:
\[ P(\text{not } C) = 1 - P(C) = 1 - \frac{1}{4} = \frac{3}{4} \]

### Step 2: Calculate the Probability of None of the Students Solving the Problem
Next, we need to find the probability that none of the students solve the problem. This can be calculated by multiplying the probabilities of each student not solving the problem:

\[ P(\text{none}) = P(\text{not } A) \times P(\text{not } B) \times P(\text{not } C \]
Substituting the values we found:
\[ P(\text{none}) = \frac{1}{2} \times \frac{2}{3} \times \frac{3}{4} \]

### Step 3: Perform the Multiplication
Now we can perform the multiplication:
\[ P(\text{none}) = \frac{1 \times 2 \times 3}{2 \times 3 \times 4} = \frac{6}{24} = \frac{1}{4} \]

### Step 4: Calculate the Probability that At Least One Student Solves the Problem
Finally, we can find the probability that at least one student solves the problem using the complement rule:
\[ P(\text{at least one}) = 1 - P(\text{none}) \]
Substituting the value we calculated:
\[ P(\text{at least one}) = 1 - \frac{1}{4} = \frac{3}{4} \]

### Final Answer
Thus, the probability that the problem will be solved by at least one of the students is:
\[ \boxed{\frac{3}{4}} \]