The probability of solving a problem of mathematic for A and B are `1/3` and `1/5` respectively. If both try the problem, find the probability that the problem will be solved.

Explanation

To solve the problem, we need to find the probability that at least one of A or B can solve the problem. We can do this by first calculating the probabilities that each person cannot solve the problem, and then using that information to find the desired probability.

### Step-by-Step Solution:

1. **Identify the probabilities of A and B solving the problem:**
- Probability that A solves the problem, \( P(A) = \frac{1}{3} \)
- Probability that B solves the problem, \( P(B) = \frac{1}{5} \)

2. **Calculate the probabilities that A and B cannot solve the problem:**
- Probability that A cannot solve the problem, \( P(A') = 1 - P(A) = 1 - \frac{1}{3} = \frac{2}{3} \)
- Probability that B cannot solve the problem, \( P(B') = 1 - P(B) = 1 - \frac{1}{5} = \frac{4}{5} \)

3. **Calculate the probability that neither A nor B can solve the problem:**
- Since A and B are working independently, the probability that neither can solve the problem is given by multiplying their individual probabilities of not solving it:
\[ P(A' \cap B') = P(A') \times P(B') = \frac{2}{3} \times \frac{4}{5} = \frac{8}{15} \]

4. **Calculate the probability that at least one of them can solve the problem:**
- The probability that at least one of A or B can solve the problem is the complement of the probability that neither can solve it:
\[ P(A \cup B) = 1 - P(A' \cap B') = 1 - \frac{8}{15} = \frac{7}{15} \]

5. **Final Result:**
- Therefore, the probability that the problem will be solved by at least one of A or B is \( \frac{7}{15} \).