# It's a KnockOut

Discrete Mathematics Level 4

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.