Prove that there are at least 50% of numbers $b$ which satisfy ${b_0}^{n-1} \not \equiv {1} \mod{n}$ if one such $b_0$ exists .

Question

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Accuracy of Fermat's Little Theorem?

$n$ is odd and composite number,and there exists $b_0$ , $0<b_0<n$ such that $gcd(n,b_0)=1$ and ${b_0}^{n-1} \not \equiv {1} \mod{n}$

prove that there are at least 50% of numbers $b$ such that $0<b<n$ and $gcd(b,n)=1$ which satisfy ${b_0}^{n-1} \not \equiv {1} \mod{n}$