<p>In a lottery all the tickets are blank except one, on which there is a prize. \(n\) persons draw a ticket each one after another without replacement. The probabilities of the 6th person to win the prize is \(\frac{6}{n}\).</p>
Step-by-Step Solution
Key Concept: By symmetry, each person has an equal probability of drawing the winning ticket regardless of draw order. The 6th person's winning probability equals 1/n, which means the statement 'probability is 6/n' is only true when n=6, revealing this is a conceptual trap about conditional vs unconditional probability.
<p><strong>Step 1 (Key Insight):</strong> Consider the symmetry of the problem. Before any draws occur, each of the n persons has an equal claim to the winning ticket.</p><p><strong>Step 2 (Conditional Probability Analysis):</strong> The 6th person wins if and only if the winning ticket is among the n tickets AND it hasn't been drawn in the first 5 draws. P(6th person wins) = P(ticket is in remaining tickets when 6th person draws) = (n-5)/n × 1/(n-5) = 1/n</p><p><strong>Step 3 (Symmetry Principle):</strong> By symmetry, P(1st wins) = P(2nd wins) = ... = P(6th wins) = ... = P(nth wins) = 1/n. This is independent of draw order.</p><p><strong>Step 4 (Verification of Given Statement):</strong> The problem states probability = 6/n. This would equal 1/n only if 6 = 1, which is false. The statement is <strong>incorrect for any value of n</strong>.</p><p><strong>Note:</strong> This appears to be a True/False or evaluation question where answer B likely represents 'False' or 'The statement is incorrect.' The correct probability is 1/n, not 6/n.</p><p>∴ Answer: B</p>
Correct Answer: B