In a multiple choice question, there are four alternative answers of which one or more than one is correct A candidate will get marks on the question only if he ticks the correct answer. The candidate decides to tick answers at a random. If he is allowed up to three chances to answer the question, then find the probability that he will get marks on it.

Explanation

To solve the problem step by step, let's break it down:

### Step 1: Understanding the Problem
We have a multiple-choice question with 4 options, and one or more of these options can be correct. The candidate can randomly tick answers and has up to 3 chances to get it right. We need to find the probability that he will get marks for the question.

### Step 2: Total Combinations of Answers
The total number of ways to choose one or more options from 4 options can be calculated using the formula for combinations. The possible combinations are:
- Choosing 1 option from 4: \( C(4, 1) = 4 \)
- Choosing 2 options from 4: \( C(4, 2) = 6 \)
- Choosing 3 options from 4: \( C(4, 3) = 4 \)
- Choosing all 4 options: \( C(4, 4) = 1 \)

So, the total number of ways to choose one or more options is:
\[ 4 + 6 + 4 + 1 = 15 \]

### Step 3: Probability of Correct Answer
Out of these 15 combinations, only 1 combination is the correct one. Therefore, the probability of getting the correct answer in one trial is:
\[ P(\text{Correct}) = \frac{1}{15} \]
And the probability of not getting the correct answer is:
\[ P(\text{Incorrect}) = 1 - P(\text{Correct}) = 1 - \frac{1}{15} = \frac{14}{15} \]

### Step 4: Probability of Getting Marks in 3 Trials
The candidate has 3 chances to get the correct answer. We can find the probability of getting at least one correct answer in these 3 trials. This can be calculated using the complement rule:
\[ P(\text{At least 1 correct in 3 trials}) = 1 - P(\text{All incorrect in 3 trials}) \]

The probability of getting all answers incorrect in 3 trials is:
\[ P(\text{All incorrect}) = P(\text{Incorrect})^3 = \left(\frac{14}{15}\right)^3 \]

Calculating \( \left(\frac{14}{15}\right)^3 \):
\[ \left(\frac{14}{15}\right)^3 = \frac{14^3}{15^3} = \frac{2744}{3375} \]

Now, substituting this back into our equation:
\[ P(\text{At least 1 correct}) = 1 - \frac{2744}{3375} = \frac{3375 - 2744}{3375} = \frac{631}{3375} \]

### Step 5: Final Probability Calculation
Thus, the probability that the candidate will get marks on the question after 3 trials is:
\[ P(\text{Marks}) = \frac{631}{3375} \]

### Conclusion
The final answer is:
\[ \text{Probability that the candidate will get marks} = \frac{631}{3375} \]