A and B are two students. Their chances of solving a problem correctly are `1/3 and 1/4`, respectively If the probability of their making a common error is, 1/20 and the obtain the same answer, then the probability of their answer to be correct is

Options

A. `1/12`
B. `1/40`
C. `13/120`
D. `10/13`

Explanation

To solve the problem step by step, we will denote the events and calculate the required probabilities.

### Step 1: Define the Events
Let:
- \( A \) be the event that student A solves the problem correctly.
- \( B \) be the event that student B solves the problem correctly.
- The probability of A solving the problem correctly is \( P(A) = \frac{1}{3} \).
- The probability of B solving the problem correctly is \( P(B) = \frac{1}{4} \).
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