Statistics And Probability Question 103
Question: In a knock out chess tournament, eight players $ P_1,P_2,…P_8 $ Participated. It is known that whenever the players $ P_{i} $ and $ P_{j} $ play, the player’s $ P_{i} $ will win j if $ i<j $ . Assuming that the players are parried at random in each round, what is the probability that the players $ P_4 $ reaches the final?
Options:
A) 31/35
B) 4/35
C) 8/35
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
Let us divide the players into two pools A and B each containing 4 players. Let $ P_4 $ be in pool A. now $ P_4 $ will reach the final if we fill the remaining three of pool A by any of $ P_5,P_6,P_7 $ or $ P_{s} $. $ \therefore $ Probability is $ \frac{^{4}C_3}{^{7}C_3}=\frac{4}{7} \times \frac{3}{6} \times \frac{2}{5}=\frac{4}{35}. $
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