<p>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 random. If he is allowed up to three chances to answer the question, then find the probability that he will get marks on it.</p>
Step-by-Step Solution
Key Concept: The candidate gets marks if at least one of the three attempts yields the correct answer set. Calculate the complement: probability of failing all three attempts, then subtract from 1.
<p><strong>Step 1:</strong> Identify the sample space. There are 4 answers, so there are 2^4 = 16 possible ways to tick (including ticking nothing). Valid attempts involve ticking at least one answer, giving 2^4 - 1 = 15 possible non-empty subsets.</p><p><strong>Step 2:</strong> Since exactly one subset is correct, probability of success in one attempt = 1/15, and probability of failure = 14/15.</p><p><strong>Step 3:</strong> With 3 independent attempts, probability of failure in all three attempts = (14/15)³ = 2744/3375.</p><p><strong>Step 4:</strong> Probability of getting marks = 1 - P(failure in all three) = 1 - 2744/3375 = 631/3375.</p><p>∴ Answer: A (or equivalent simplified form: <strong>631/3375</strong>)</p>
Correct Answer: A