Lets assume that a team plays 50 games in a season and has a probability of 67% to win each individual game and 33% to lose each of these games (Games are Independent). I want to create a hypothesis test to determine whether or not the team will lose back to back games in a season (null is that they don't ever lose back to back games in a season and alternate is that they do lose at least 1 set of back to back games in the season). So I am assuming I would set Ho=0 and H1 > 0 to indicate back to back losses, but then I am a little stumped about setting up the test statistic for this problem.
Then once I solve the hypothesis test, I need to estimate the actual probability that the team will not lose back to back games. At first I thought I could use a confidence interval to do this, but I don't think that will work. What are some ways I can go about doing this?
In addition to this, are there any other ways besides hypothesis tests (or Monte Carlo simulations which I have already done) to go about solving this type of problem? I am essentially just trying to learn various ways to solve these types of problems statistically so your help is appreciated.