Question

You have a fair coin and you want to simulate an event that has probability 1/3, and an event that has probability 2/3. How do you do it?

Answer 1

You can simulate any probability between 0-1 with a coin if you do enough flips to assign the possibility of the combinations appearing as an event, always taking into consideration that if you want to represent an event of
`(x)/(y)`, y would have to be something
`2^(n)` or you will need to take one of the set of flips as "try again", where 2 represents the number of equal possibilities in a fair coin (head and tails, so 2 possibilities) and n is the number of flips.

Let's take the numbers given in the problem as examples, you want to represent 1/3 and 2/3. So the number that comes closer to the denominator is
`2^(2)`=4 or two flips.

This gives of the events:

HH

HT

TH

TT

Each with 1/4 chance of appearing, but we ant 1/3 and 2/3. We can simulate it by making:

HH - 1/3

HT - 1/3

TH - 1/3

TT - "Try again"

We can then make any two combinations of the first three the 2/3, and the other one 1/3. For example, HH would be 1/3 and either HT or TH 2/3. If TT appears after 2 flips, you will just need to flip two times again.