Researchers at a large midwestern university have developed algorithms to detect when a submitted assignment was written by artificial intelligence $($AI$)$ instead of by the student. The researchers have shown that these algorithms correctly identified a non$-$AI $($student$-$written$)$ submission $98\mathrm{.}3\%$ of the time and correctly identified use of an AI $94\mathrm{.}7\%$ of the time. Note that students are assumed to not have plagiarized using an AI until evidence of AI use has been detected.

$1.$ What is the probability of making a Type I error $(\backslash$alpha $)$ in the "Detecting AI Plagiarism" scenario? $[$Express your answer as a decimal, not percentage.$]$

$2.$Describe what a Type I error would mean in the terms of the "Detecting AI Plagiarism" scenario.

$3.$What is the probability of making a Type II error $(\backslash$beta $)$ in the "Detecting AI Plagiarism" scenario? $[$Express your answer as a decimal, not percentage.$]$

$4.$Describe what a Type II error would mean in the terms of the "Detecting AI Plagiarism" scenario.