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?

• pbty of winnin+pbty of losin= (2/3)*(2/3) +(1/3)*(1/3)
  =4/9 +1/9
  =5/9
• 13 years agoHelpfull: Yes(59) No(4)
• chance 0f A wins = 2/3
  prediction of octopus is also = 2/3(given in ques)
  chance of b wins = 1/3
  octopus prediction = 1/3
  2/382/3 = 1/381/3 = 5/9
• 13 years agoHelpfull: Yes(32) No(9)
• 5/9
• 13 years agoHelpfull: Yes(12) No(11)
• total probability is either if Ghana wins then Bolivia loses or if Bolivia wins Ghana loses.so,
  total probability=[[p(Ghana win's]*p[Bolivia loses]]+[[p(Bolivia win's]*p[Ghana loses]].
  =[(2/3*1/3)+(1/3*2/3)]=4/9.
• 10 years agoHelpfull: Yes(8) No(3)
• So Paul predicts the team with same probability , as the chances of the team winning (given).
  Probability of Ghana winning is 2/3 (given).
  As per the above two statements above the probability of Paul correctly predicting i,e the probability of Paul picking ghana and Ghana winning will be 2/3*2/3=4/9.
  On same lines that of Ghana is 1/3*1/3=1/9.
  Now probability of Paul correctly predicting result is= probability of Paul correctly predicting Ghana+ probability of Paul correctly predicting Bolivia=4/9+1/9=5/9
  Ans-5/9
• 8 years agoHelpfull: Yes(7) No(0)
• 2/3 as it is given in the answer that the paul selects the team with the same probability in which the team will win...
• 13 years agoHelpfull: Yes(4) No(38)
• tot prob=octo chooses correct+octo chooses wrong
  =2/3*2/3+1/3*2/3=6/9
  correct ans chos by octo=2/3*2/3=4/9
  prob=4/6=2/3.
• 9 years agoHelpfull: Yes(0) No(2)
• Ans is 5/9
• 9 years agoHelpfull: Yes(0) No(0)