Question

Assume a team plays 6 games. If the team is equally likely to win as to lose each game, what is the probability that they win a string of at least 4 games in a row? I found my sample size to be 2^6=64 and I've tried listing out all the sequences, what I found was. W W W W W W ; W W W W W L ; W W W W L L ; L W W W W L ; L W W W W W ; L L W W W W

Answer 1

There are only 3 ways to have a 4-game winning streak, 2 ways to have a 5-game winning streak and 1 way to have a 6-game winning streak, for a total of 6 ways to win at least 4 games in a row.

You've pointed out that there are \(2^6\) possible game records, so the probability of a least a 4-game winning streak is \(\cfrac{6}{2^6}\), not very likely.

Let me know if you have any questions.