I came up with this problem the other day. I don’t have nearly enough math to solve it. Do any of you wise folk have insight?
Imagine a sequence of randomly generated 0s and 1s. I start from nothing and generate this sequence one term at a time. I stop when I’m at the end of a streak of 1s which is at least one half the length of the total sequence.
For example:
01
0010110101101011111111111111
010110111111 -EDIT: Obviously, this is wrong, because it would terminate at 01. Sorry.
What is the average length of such sequences?
I know that all of these sequences will eventually terminate. I just don’t know if the length diverges, and I’m not sure how to deal with the problem.
Tricksy probability problem
I came up with this problem the other day. I don’t have nearly enough math to solve it. Do any of you wise folk have insight?
Imagine a sequence of randomly generated 0s and 1s. I start from nothing and generate this sequence one term at a time. I stop when I’m at the end of a streak of 1s which is at least one half the length of the total sequence.
For example:
01
0010110101101011111111111111
010110111111 -EDIT: Obviously, this is wrong, because it would terminate at 01. Sorry.
What is the average length of such sequences?
I know that all of these sequences will eventually terminate. I just don’t know if the length diverges, and I’m not sure how to deal with the problem.