Compute posterior fake probability using Bayes' rule

A platform employs an automated detector to flag fake accounts.

• Prior probability of a fake account: $P(F)=0.02$.
• True positive rate, also called sensitivity: $P(\text{Flag}\mid F)=0.90$.
• False positive rate: $P(\text{Flag}\mid\neg F)=0.05$. Given a flagged account, what is the probability that it is actually fake, $P(F\mid \text{Flag})$? Show your calculation. Overview: The question assesses Bayes' rule and conditional probability in the Statistics & Math domain for a Data Scientist position, at an introductory applied probability/interpretation level.