16. a) Show that the probability that $n$ is a strong pseudoprime for a base $b$ randomly chosen with $1 \leqslant b \leqslant n-1$ is near $(n-1) / 4$ only when $n$ has a prime factorization of the form $n=p_{1} p_{2}$ where $p_{1}=1+2 q_{1}$ and $p_{2}=1+4 q_{2}$ with $q_{1}$ and $q_{2}$ prime or $n=p_{1} p_{2} p_{3}$ where $p_{1}=1+2 q_{1}$, $p_{2}=1+2 q_{2}, p_{3}=1+2 q_{3}$ with $q_{1}, q_{2}, q_{3}$ distinct odd primes.
b) Find the probability that $n=49939.99877$ is a strong pseudoprime to the base $b$ randomly chosen with $1 \leqslant b \leqslant n-1$.