A few days ago i had an argument with a friend about this question :
What is the probability of getting 6 heads in a row from 200 flips ?
I argued it is high probability (significantly bigger than half) while he argued it is low probability.
When i tried to give exact formula i failed so we checked the web were the answer was about 84%, yet he is still not convinced so from this i have two questions:
1) What is the exact formula for $k$ Heads in a row (consecutive) out of $n$ coin flips?
2) (Not a mathematical) How to convince my friend that 6 in a row have high probability ? meaning what is the intuition behind the question ?