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GATE 2014 EE (EE1) – Question 37

Engineering Mathematics · Probability and Statistics: Random variables · 2 marks · Multiple choice

A fair coin is tossed n times. Find the probability that the difference between heads and tails counts is n − 3.

  1. $2^{-n}$
  2. $0$
  3. $\binom{n}{n-3}2^{-n}$
  4. $2^{-n+3}$

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Correct answer: (B) $0$

Explanation

With Hheads and Ttails, H+T=nand H−T=n−3would imply2H=2n−3. The right side is odd, while2Hmust be even. The event is impossible for every integer n, so probability is **0,B**. The same parity obstruction holds if difference means absolute difference.