What's the probability of getting at least 3 concecutive heads in 10 tosses of a coin?

[JoJo1234]

If I toss a coin 10 times, what's the probability of getting at least 3 heads concecutively? The results of the other 7 tosses do not matter. Please show me the formula as well as the result, thank you!

 

[katxt]

Try listing the possibilities. hhh thhh tthhh etc Find the probability of each one. Add them up.

 

[JoJo1234]

Thanks for the reply.
Since there is a myriad of possibilities for the other 7 tossses,I don't think simply listing the possibilities would work because there is too much work involved.

 

[katxt]

Yeah, you're right. There are quite a few. I didn't think it quite through. I'll have another ponder. kat

 

[spunky]

If I toss a coin 10 times, what's the probability of getting at least 3 heads concecutively? The results of the other 7 tosses do not matter. Please show me the formula as well as the result, thank you!

This seems useful and relevant to your question

 

[katxt]

This seems useful and relevant to your question -
https://www.quora.com/If-you-flip-a...r-tails-in-a-row/answer/Christopher-Pellerito
http://wangling.me/2008/09/the-probability-of-runs-of-k-consecutive-heads-in-n-coin-tosses.html

 

[JoJo1234]

This seems useful and relevant to your question -
https://www.quora.com/If-you-flip-a...r-tails-in-a-row/answer/Christopher-Pellerito
http://wangling.me/2008/09/the-probability-of-runs-of-k-consecutive-heads-in-n-coin-tosses.html

Thank you for the help katxt

 

[katxt]

It's not an easy problem. It looks like there is no formula. To get 3 out of 10 you first have to work out 3 out of 9 and 2 out of 9 and combine them.