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Q2) 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
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Answer / desikan
d. (2/3)^10 + 8/3*(2/3)^9
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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