How to set up an event with probability of one seventh from coin tossing? I have been recently asked in an interview a question that: How to set up an event with probability of one seventh from coin tossing?
I couldn't find the correct answer and still don't know the correct answer yet.
 A: What about you toss 3 coins giving the possible events
$$
{TTT,TTH,THT,HTT,HHT,HTH,THH,HHH}
$$
Let event B = not all heads
and event A = All tails
then
$$
P(A|B) = \frac{P(B|A)P(A)}{P(B)}=\frac{1*1/8}{7/8}=1/7
$$
A: I assume they mean fair coins, o/w the answer would be trivial. And, I humbly think that this is a brain teaser problem and the hidden question is: write $1/7$ in binary, i.e. $0.0010010...$.
For example, an event with probability $1/4+1/8=3/8=0.011$, can be constructed with the following small events: $\{TTT,TTH,HHH\}$, i.e. what is the probability of having first two tosses as Tails, or having first three tosses as Heads. 
This yields in infinite number of experiments for obtaining $1/7$. But, we can get arbitrarily close. So, achieving $1/7$ is probably (and only) possible under a recursive setting, but that seemed hard for an interview.
A: According to this article https://mindyourdecisions.com/blog/2017/01/01/can-you-solve-it-use-a-coin-to-simulate-any-probability-sunday-puzzle/.
Create a game like this:
HHH: you win
TTT: re-toss.
HHT, HTH, HTT, THH, THT, TTH: you lose.
Your probability to win is 1/7.
Using the same method, we can simulate probability of any non-irrational number.
