I just got this basic probability question in an interview. I am a bit rusty with my probability and surely got it wrong.

What is a proper way to solve this problem? The more basic the calculation, the better - interview and all that.

In case the question isn't clear from the title: How many times must a fair coin be flipped to have 90% confidence that at least one heads has been the result?


Assume fair coin and independent tosses. Probability of k tails in a row is

$$(1/2)^k$$ and you want the smallest $k$ such that

$$(1/2)^k \leq (1/10),\quad i.e.,\quad 2^k\geq 10$$

So $k=4$ tosses are needed.


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