Probability that two randomly generated strings are not identical

Hello

Please help me with the below problem

A random string of length n is constructed by tossing a fair coin n times and setting a bit to 0(heads) or 1(tails).
Probability that two randomly generated strings are not identical is ______

I have :
P(not identical) = 2^n (each place can be filled in two ways)

given ans: 1-1/(2^n)

Thanks

mathdaemon said:

A random string of length n is constructed by tossing a fair coin n times and setting a bit to 0(heads) or 1(tails).
Probability that two randomly generated strings are not identical is ______

given ans: 1-1/(2^n)

Click to expand...

\(\displaystyle \mathcal{P}(\text{being identical})=\dfrac{1}{2^n}\).

So \(\displaystyle \mathcal{P}(\text{not being identical})=1-\dfrac{1}{2^n}\).

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