How can you create a uniform distribution from 1 to 200 using an unbiased coin?

Question

Accepted Answer

To create a uniform distribution from 1 to 200 using an unbiased coin, we can use the rejection sampling method.

Divide the range into equal parts based on the number of outcomes of the coin toss.
Toss the coin and select the corresponding part of the range.
If the selected number is outside the desired range, reject it and repeat the process.
Repeat until a number within the desired range is obtained.
Example: If the coin has 2 outcomes, divide the range into 2 parts of 100 each.
If the coin lands on heads, select the first part of the range (1-100).
If the selected number is 150, reject it and repeat the process.
If the selected number is 75, accept it and stop the process.

Goldman Sachs Analyst interview questions & answers