Chips in a Bag

What this probability-inference interview question tests

This is an easy probability question that requires you to work backwards from an observed probability to infer the composition of a population. It is the kind of problem quant traders and researchers encounter when reasoning about market regimes or hidden states from limited data.

The core skill is setting up an equation for the probability of a compound event (drawing two items without replacement) and solving for an unknown parameter. The question rewards clear algebraic reasoning and the ability to recognize that the constraint must yield a unique, sensible answer.

• Sampling without replacement and conditional probability
• Working from a known probability back to the population parameter
• Checking that your solution is consistent with the problem constraints