In a multiple choice question there are 4 alternative answers of which 1, 2, 3, or all may be correct. A candidate will get marks in the question only if he ticks all the correct answers. The candidate decides to tick answers at random. If he is allowed upto 5 chances to answer the question, the probability that he will get the marks in the question is

Options

A. `1//5`
B. `5//14`
C. `3//5`
D. 1

Answer

To solve the problem, we need to calculate the probability that a candidate will correctly mark all the correct answers in a multiple-choice question with 4 options (A, B, C, D), given that he can make up to 5 attempts.

### Step-by-Step Solution:

1. **Identify the Total Number of Options**:
The question has 4 options: A, B, C, and D. Each option can either be correct or incorrect.

2. **Determine the Total Combinations**:
Each of the 4 options can either be selected or not selected. Therefore, the total number of ways to select options is \(2^4 = 16\). This includes all combinations of selecting none, one, two, three, or all four options.

3. **Identify the Favorable Outcomes**:
We need to identify how many of these combinations are correct.
- If there are no correct answers, there is 1 way (select none).
- If there is 1 correct answer, there are 4 ways (A, B, C, or D).
- If there are 2 correct answers, there are \( \binom{4}{2} = 6 \) ways (AB, AC, AD, BC, BD, CD).
- If there are 3 correct answers, there are \( \binom{4}{3} = 4 \) ways (ABC, ABD, ACD, BCD).
- If all 4 answers are correct, there is 1 way (ABCD).

Therefore, the total number of favorable outcomes (where the candidate marks all correct answers) is:
- 1 (0 correct) + 4 (1 correct) + 6 (2 correct) + 4 (3 correct) + 1 (4 correct) = 16.

4. **Calculate the Probability of Getting Marks in One Attempt**:
The probability of getting the marks in one attempt (i.e., selecting all correct answers) is given by the number of favorable outcomes divided by the total outcomes:
\[ P(\text{correct in one attempt}) = \frac{1}{16} \]

5. **Calculate the Probability of Getting Marks in 5 Attempts**:
The probability of not getting the marks in one attempt is:
\[ P(\text{not correct in one attempt}) = 1 - P(\text{correct in one attempt}) = 1 - \frac{1}{16} = \frac{15}{16} \]
The probability of not getting the marks in 5 attempts is:
\[ P(\text{not correct in 5 attempts}) = \left(\frac{15}{16}\right)^5 \]
Therefore, the probability of getting at least one correct answer in 5 attempts is:
\[ P(\text{at least one correct in 5 attempts}) = 1 - P(\text{not correct in 5 attempts}) = 1 - \left(\frac{15}{16}\right)^5 \]

6. **Final Calculation**:
Now, we compute \( \left(\frac{15}{16}\right)^5 \):
\[ \left(\frac{15}{16}\right)^5 \approx 0.735 \]
Therefore, the probability of getting at least one correct answer in 5 attempts is:
\[ P(\text{at least one correct in 5 attempts}) \approx 1 - 0.735 = 0.265 \]

### Conclusion:
The probability that the candidate will get marks in the question by ticking all correct answers in up to 5 chances is approximately \(0.265\).