“You pull one of two coins (fair or double-headed) and flip heads. Probability it is the double-headed coin? After a second heads?”
What they test. Bayes and sequential updating
Weak answer. Probably more likely double-headed, so maybe 66%, then 75-80%.
Strong answer. P(D|H1) = (1 x 0.5) / ((1 x 0.5) + (0.5 x 0.5)) = 0.5/0.75 = 2/3. After a second heads, P(D|H1,H2) = (1 x 0.5) / ((1 x 0.5) + (0.25 x 0.5)) = 0.5/0.625 = 4/5 = 80%.