The probability of solving a problem by three students are `1/3,1/4,1/5`. Find the probability that the problem will be solved if all three students try the problem simultaneously.

Explanation

To solve the problem, we need to find the probability that at least one of the three students solves the problem when they all try to solve it simultaneously. We can approach this using the concept of complementary probability.

### Step-by-Step Solution:

1. **Identify the probabilities of each student solving the problem:**
- Let \( P(A) \) be the probability that student A solves the problem:
\[ P(A) = \frac{1}{3} \]
- Let \( P(B) \) be the probability that student B solves the problem:
\[ P(B) = \frac{1}{4} \]
- Let \( P(C) \) be the probability that student C solves the problem:
\[ P(C) = \frac{1}{5} \]

2. **Calculate the probabilities of each student not solving the problem:**
- The probability that student A does not solve the problem:
\[ P(A') = 1 - P(A) = 1 - \frac{1}{3} = \frac{2}{3} \]
- The probability that student B does not solve the problem:
\[ P(B') = 1 - P(B) = 1 - \frac{1}{4} = \frac{3}{4} \]
- The probability that student C does not solve the problem:
\[ P(C') = 1 - P(C) = 1 - \frac{1}{5} = \frac{4}{5} \]

3. **Calculate the probability that none of the students solve the problem:**
- Since the events are independent, the probability that none of the students solve the problem is:
\[ P(A' \cap B' \cap C') = P(A') \times P(B') \times P(C') = \frac{2}{3} \times \frac{3}{4} \times \frac{4}{5} \]
- Now, calculate this product:
\[ P(A' \cap B' \cap C') = \frac{2 \times 3 \times 4}{3 \times 4 \times 5} = \frac{24}{60} = \frac{2}{5} \]

4. **Calculate the probability that at least one student solves the problem:**
- The probability that at least one of the students solves the problem is the complement of the probability that none of them solve it:
\[ P(A \cup B \cup C) = 1 - P(A' \cap B' \cap C') = 1 - \frac{2}{5} = \frac{3}{5} \]

### Final Answer:
The probability that the problem will be solved if all three students try the problem simultaneously is:
\[ \frac{3}{5} \]