A certain soccer team starts the season with the coach named Pep. The team wins any particular match with probability 2=3 independently of all other matches. Pep will get red when the team loses for the second time. Then a substitute coach Tito is hired and he will get a raise when the team wins for the third time after he got hired. Assume that one game is played every week. Find the expected number of weeks that Tito will have to wait from the start of the season and before he gets his raise. Solution 10 weeks or 11 weeks First 6 weeks they face the second loss and replacement of coach pep After 3 more weeks they have won 2 times and 1 loss So either the 10 or 11th week they have their third win and hence the answer is 10 or 11.