Recognize this as a Bayes' theorem problem and set up the calculation using the given probabilities. Compute the probability of a story being real and having 100+ likes, then divide by the total probability of having 100+ likes (summing over real and fake stories).
Pro tip: After calculating, sanity-check the result: since fake stories are much more likely to get 100+ likes, the posterior probability of real should be lower than the prior (70%). This helps catch errors.
Let R be the event that a story is real, F that it's fake, and L that it has 100+ likes. Write down P(R)=0.7, P(F)=0.3, P(L|F)=0.8, P(L|R)=0.08.
Calculate P(R and L) = P(R)*P(L|R) = 0.7*0.08 = 0.056. Calculate P(F and L) = P(F)*P(L|F) = 0.3*0.8 = 0.24.
Sum the joint probabilities: P(L) = P(R and L) + P(F and L) = 0.056 + 0.24 = 0.296.
Compute P(R|L) = P(R and L) / P(L) = 0.056 / 0.296 ≈ 0.1892, or about 18.9%.
The probability is about 18.9%, which is lower than the prior 70%, as expected because fake stories are much more likely to get 100+ likes. This makes sense.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.