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1. Refreshing on Bayesian. Two boxes of balls. First box has 10 red balls and 30 green balls. The second one has 20 reds and 20 greens. What's the probability of a person (randomly) choosing the first box? Yes, 50%. That's true if you haven't observed anything prior to answering that question. But, suppose you saw a person randomly chose a box (either one) then randomly picked a ball (either one), and as it turned out he got a green. Now, I ask you again: What's the probability of that person (randomly) choosing the first box? Now you become subjective. Conditional on your having seen him got a green, you will go: "Ehm, I guess it is more likely that he chose the first box, not the second box". That is, you're saying: it's more than 50% (because you know, the first box has more greens). Indeed, using Bayesian approach, it is 60%. Why? The conditional probability of randomly picking up a green from the first box is 75%, and from the second box 50%. The prior probability of randomly choosing each box is 50%. Bayesian Theorem says, the posterior probability (or, subjective probability, if you like) of choosing the first box, given that you saw him hold a green is the joint probability of (a priori-ly) choosing the first box and getting a green out of it, divided by the sum of both joint probabilities. That is, 60% = (50%*75%) : [(50%*75%)+(50%+50%)].