Classic Bayes setup but I fumbled the denominator at first.
Recognize this as a Bayes' theorem problem and define the events clearly: F for fake, L for 100+ likes. Compute the total probability of L using the law of total probability, then apply Bayes' theorem to find P(F|L).
Pro tip: After calculating, sanity-check the result: since fake posts are much more likely to get 100+ likes, the posterior should be significantly higher than the prior (30%). Also, briefly explain the intuition to show you understand the result, not just the math.
Let F be the event that a post is fake, and L be the event that it gets 100+ likes. Write down P(F) = 0.30, P(L|F) = 0.80, and P(L|F^c) = 0.08.
Use the law of total probability: P(L) = P(L|F)P(F) + P(L|F^c)P(F^c) = 0.80*0.30 + 0.08*0.70 = 0.24 + 0.056 = 0.296.
Compute P(F|L) = P(L|F)P(F) / P(L) = 0.24 / 0.296 ≈ 0.8108, or about 81.1%.
Note that the probability is much higher than the prior 30%, which makes sense because fake posts are far more likely to get 100+ likes. Verify the calculation and consider if the result is reasonable.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.