A random bit string of length n is constructed by tossing a fair coin n times…

GATE · 2005 · CS

A random bit string of length n is constructed by tossing a fair coin n times and setting each bit to 0 or 1 depending on whether the outcome is head or tail, respectively. What is the probability that two such randomly generated strings are not identical?

  1. A.

    1/2^n

  2. B.

    1 - (1/n)

  3. C.

    (1/n!)

  4. D.

    1 - 1/2^n

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