In an objective paper, there are two sections of 10 questions each.For "section 1", each question has 5 options and only one optionis correct and "section 2" has 4 options with multiple answers and marks for a question in this section is awarded only if he ticks all correct answers. Marks for each question in "sectionl 1" is 1 and in "section 2" is 3. (There is no negative marking.) If a candidate attempts only two questions by guessing, one from "section 1" and one from "section 2", the probability that he scores in both question is `74/75`

Options

A. `74//75`
B. `1//25`
C. `1//15`
D. `1//75`

Explanation

To solve the problem step by step, we need to calculate the probability of scoring in both sections when a candidate guesses one question from each section.

### Step 1: Calculate the Probability for Section 1
In Section 1, there are 5 options for each question, and only one of them is correct. Therefore, the probability of guessing the correct answer is:

\[ P(\text{Correct in Section 1}) = \frac{1}{5} \]

### Step 2: Calculate the Probability for Section 2
In Section 2, there are 4 options, and multiple answers can be correct. We need to find the total number of ways to select the correct answers:

1. **One option correct**: There are 4 ways (choose 1 from 4).
2. **Two options correct**: The combinations are:
- (1, 2)
- (1, 3)
- (1, 4)
- (2, 3)
- (2, 4)
- (3, 4)
This gives us a total of 6 ways.
3. **Three options correct**: The combinations are:
- (1, 2, 3)
- (1, 2, 4)
- (1, 3, 4)
- (2, 3, 4)
This gives us a total of 4 ways.
4. **All options correct**: There is only 1 way (1, 2, 3, 4).

Now, we sum these possibilities to find the total number of ways to select the correct answers in Section 2:

\[ \text{Total ways} = 4 + 6 + 4 + 1 = 15 \]

Thus, the probability of guessing the correct answer in Section 2 is:

\[ P(\text{Correct in Section 2}) = \frac{1}{15} \]

### Step 3: Calculate the Combined Probability
To find the probability that the candidate scores in both questions (one from each section), we multiply the probabilities from both sections:

\[ P(\text{Correct in both sections}) = P(\text{Correct in Section 1}) \times P(\text{Correct in Section 2}) = \frac{1}{5} \times \frac{1}{15} = \frac{1}{75} \]

### Conclusion
The final probability that the candidate scores in both questions is:

\[ \frac{1}{75} \]