# Probability Question

• August 21st 2007, 07:10 AM
Freyalise
Probability Question
Hi guys, first time poster. I hope this section is the most appropriate for my problem - please feel free to move it if it is too basic :)

A fair coin is flipped n times.

What is the probability that there are at least k consecutive heads in these flips?

If the k-generalisation is making the working awkward then please just solve it for k = 2 because I think I know how to get from there to the general answer.

Thanks for any help you can give me!
• August 21st 2007, 09:08 AM
JakeD
Quote:

Originally Posted by Freyalise
Hi guys, first time poster. I hope this section is the most appropriate for my problem - please feel free to move it if it is too basic :)

A fair coin is flipped n times.

What is the probability that there are at least k consecutive heads in these flips?

If the k-generalisation is making the working awkward then please just solve it for k = 2 because I think I know how to get from there to the general answer.

Thanks for any help you can give me!

It looks to me like you want $1 - P(M_n^{(k)} = 0)$ from Theorem 1 in this paper.

This was found by googling Bernoulli trials success runs.
• August 21st 2007, 01:42 PM
Freyalise
Thank you very much.

My Maths is not marvellous so that paper will need some study but it looks like exactly what I need. I'm glad the problem was nontrivial after all at least.