It's a KnockOut
8 players: \(p_1,p_2,p_3,p_4,p_5,p_6,p_7\) and \(p_8\) play a knock out tournament. It is known that if players \(p_i\) and \(p_j\) play, \(p_i\) always wins if \(i<j\). Suppose that players are paired at random in each round, find the probability that player \(p_4\) reaches the final.
Give your answer to 3 decimal places.
Also try : How could it be so Probable