In a game of six digits, two digits are already fixed for prize. If any one will find these two fixed digits then he will win the prize. Mr. A selects two numbers. The probability that Mr. A will win the prize is

Options

A. `1/15`
B. `1/6`
C. `1/5`
D. `1/1`

Answer

To find the probability that Mr. A will win the prize by selecting the two fixed digits in a game of six digits, we can follow these steps:

### Step-by-Step Solution

1. **Understand the Total Digits and Winning Digits**:
- There are a total of 6 digits, out of which 2 digits are fixed as winning digits.

2. **Calculate the Probability of Selecting the First Winning Digit**:
- The probability of selecting one of the winning digits on the first attempt:
\[ P(\text{First winning digit}) = \frac{\text{Number of winning digits}}{\text{Total digits}} = \frac{2}{6} = \frac{1}{3} \]

3. **Calculate the Probability of Selecting the Second Winning Digit**:
- After selecting one winning digit, there will be 5 digits left (1 winning digit and 4 non-winning digits).
- The probability of selecting the second winning digit on the second attempt:
\[ P(\text{Second winning digit}) = \frac{\text{Remaining winning digits}}{\text{Remaining total digits}} = \frac{1}{5} \]

4. **Calculate the Total Probability of Winning**:
- Since both selections need to happen for Mr. A to win, we multiply the probabilities of both events:
\[ P(\text{Winning}) = P(\text{First winning digit}) \times P(\text{Second winning digit}) = \frac{1}{3} \times \frac{1}{5} = \frac{1}{15} \]

5. **Conclusion**:
- Therefore, the probability that Mr. A will win the prize by selecting the two fixed digits is:
\[ \frac{1}{15} \]