You flip a coin 10 times and if it lands "heads" 4 or more times in a row is considered a success. What is the probability of a success?
(Someone asked this a few hours ago and I worked out a computer simulation and quite recently I used Excel to get the exact probability.
Of the 2^10 (or 1,024) possible ways that 10 coin tosses can occur, 251 are success (so p=0.2451171875).
Basically, I know there is a simpler way to do this (and it doesn't require Markov chains) so, what is a neater way to solve this?

Question

You flip a coin 10 times and if it lands "heads" 4 or more times in a row is considered a success.  What is the probability of a success?
(Someone asked this a few hours ago and I worked out a computer simulation and quite recently I used Excel to get the exact probability.
Of the 2^10 (or 1,024) possible ways that 10 coin tosses can occur, 251 are success (so p=0.2451171875).
Basically, I know there is a simpler way to do this (and it doesn't require Markov chains) so, what is a neater way to solve this?

wolf1728 · Answer

If it helps here is the Excel spreadsheet that shows all of the 251 successes out of the 1,024 possibilities.