I can’t reproduce your problem:
julia> float(binomial(big(100),50) // big(2)^100)
7.95892373871787614981270502421704614029315404247333213573478705171737601631321e-02
Can you try it in a fresh Julia session?
I can’t reproduce your problem:
julia> float(binomial(big(100),50) // big(2)^100)
7.95892373871787614981270502421704614029315404247333213573478705171737601631321e-02
Can you try it in a fresh Julia session?