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