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Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

chelsea v arsenal
In the FA Cup 64 teams play a knockout tournament. Over the four years 2001, 2002, 2003 and 2004 Arsenal have been drawn against Chelsea each year and have beaten Chelsea every time. What is the probability of that happening?

Let's say that whenever Arsenal and Chelsea play the probability of Arsenal winning is 0.6 and otherwise, throughout the tournament, both these teams have a probability of winning of 0.7 in the first round, 0.6 in the second round and 0.5 in the subsequent rounds.