# random variable with binomial distribution

I have a probability space $\omega = 2^{\{1,\ldots,n\}}$ $\sigma$-algebra $2^\omega$ and $P(\{s\})=(p^{|s|})*(1-p)^{(n-|s|)}$

I assume that $n=2k$,$k$ natural number

I need to find a random variable that will distribute like $\mathrm{Bin}(k,p^2)$

Can you help me with this please?

Thanks.
benny

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Hint: $2 = n/k$.
Another hint: $p^2$ has the same exponent $2$ as $n/k$.