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Quantitative Aptitude :: Probability - Discussion

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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?





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Answer: 5/9

Solution: Answer is 5/9 because for example

Let Paul picks Ghana then probability that its prophecy will be true is 2/3*2/3 =4/9.

Now it may pick up Bolivia and the chances of winning are 1/3*1/3=1/9

So total probability will be 4/9 1/9=5/9

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