Probability that India wins the World Cup

Paul, the octopus who has been forecasting the outcome of FIFA world cup matches with tremendous accuracy has now been invited to predict ICC world cup matches in 2011. We will assume that the world cup contenders have been divided into 2 groups of 9 teams each. Each team in a group plays the other teams in the group. The top two teams from each group enter the semi finals (after which the winner is decided by knockout).
However, Paul has a soft spot for India and when India plays any team, Paul always backs India. Alas, his predictions on matches involving India are right only 2 out of 3 times. In order to qualify for the semi finals, it is sufficient for India to win 7 of its group matches. What is the probability that India will win the ICC world cup?
This question is related to TCS Interview

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Avik Dasgupta

  • Dec 17th, 2010
 

We have two chances to win the world cup.  

Either India can win all 10matches or Win 7 out of 8 group matches + win the semi final and final matches. 
Case 1: To win all 10, probability is (2/3)^10. 
Case 2: Probability of winning 7mathces out of 8= (2/3)^7 and 
Probability of Loosing the 1 match= 1/3. 
This process can occur in 8 ways. 
probability= 8*((2/3)^7 * 1/3) 
To win semi final and final match probability is (2/3)^2 
Total probability=8*((2/3)^7 * 1/3) * (2/3)^2 = 8/3 * (2/3)^9. 
So total probability, Case1+Case 2= (2/3)^10 + 8/3 * (2/3)^9

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