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A random bit string of length n is constructed by tossing a fair coin n times and setting a bit to 0 or 1 depending on outcomes head and tail, respectively. The probability that two such randomly generated strings are not identical is
  • a)
    1/2
  • b)
    1-1/n
  • c)
    1/n!
  • d)
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
A random bit string of length n is constructed by tossing a fair coin...
Since the coin is fare, P(H) = P(T) = 1/2
Length of the string = n
P(X) = both the strings should not be identical
P(-X) = both are not identical = 1 – P(X)
If both the strings are equal, every character should be same w.r.t. its positions.
i.e. P(X) = (1/2)×(1/2)× … n times = (1/2)n
P(-X) = 1 – (1/2)n
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A random bit string of length n is constructed by tossing a fair coin n times and setting a bit to 0 or 1 depending on outcomes head and tail, respectively. The probability that two such randomly generated strings are not identical isa)1/2b)1-1/nc)1/n!d)Correct answer is option 'D'. Can you explain this answer?
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