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

I THINK A

Explanation:

Answer 2

There is 1 way to win 6 games in a row wwwwww There are 2 ways to win 5 games in a row wwwwwl, lwwwww There are 5 ways to win 4 games in a row llwwww, wwwwll, lwwwwl, wlwwww, and wwwwlw. There are 2^n to arrange 6 wins and losses which adds up to 2^(6) = 64 So the Probability they win all four games in a stretch is 5 + 2 + 1 ways = 8 ways. So the probability = 8/64 = 1/8