A space$-$ship operator is having problems with imposters boarding their spaceships and disrupting the crew. The government has developed a powerful $$risk$-$scoring algorithm$$ to catch imposters before they board a spaceship. It is estimated that for every imposter who tries to board a spaceship, there are $100,000$ crew$-$members who are perfectly safe, posing no threat to security. $($In other words, the probability that any given crew$-$member is an imposter is $1$ in $100,001.)$ This risk$-$scoring algorithm is $100\%$ sensitive$,$ i$.$e$.,$ it will correctly identify an imposter $100\%$ of the time. This risk$-$scoring algorithm is $99\%$ specific, i$.$e$.,$ it will correctly allow a non$-$imposter to board a spaceship $99\%$ of the time, but will incorrectly identify that crew$-$member as an imposter $1\%$ of th