For the FIFA world cup, Paul the octopus has been predicting the winner of each match with amazing success. It is rumored that in a match between 2 teams A and B, Paul picks A with the same probability as A's chances of winning. Let's assume such rumors to be true and that in a match between Ghana and Bolivia, Ghana the stronger team has a probability of 2/3 of winning the game. What is the probability that Paul will correctly pick the winner of the Ghana-Bolivia game?
Options
A) 1/9  B) 4/9  C) 5/9  D) 2/3  E) 1/3
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   = 5/9   ANSWER:5/9
<result>C</result>
For the FIFA world cup, Paul the octopus has been predicting the winner of each match with amazing success. It is rumored that in a match between 2 teams A and B, Paul picks A with the same probability as A's chances of winning. Let's assume such rumors to be true and that in a match between Ghana and Bolivia, Ghana the stronger team has a probability of 2/3 of winning the game. What is the probability that Paul will correctly pick the winner of the Ghana-Bolivia game?