For the FIFA world cup, Paul the octopus has been predicting the winner of each match with amazingsuccess. It is rumored that in a match between 2 teams A and B, Paul picks A with the same probability as A’schances of winning.Let’s assume such rumors to be true and that in a match between Ghana and Bolivia, Ghana the stronger teamhas a probability of 2/3 of winning the game. What is the probability that Paul will correctly pick the winner ofthe Ghana-Bolivia game?
Paul picks A with the same probability as A’schances of winning
So probability of picking a winner = prob picking of ghana * ghana winning + prob picking of bolivia * bollivia winning
= 2/3 * 2/3 + 1/3 * 1/3
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