Prime Time Payout

What this probability and expected value interview question tests

This is a medium-difficulty probability question commonly used in first-round interviews at quantitative trading firms. It combines two core skills: enumerating outcomes from a discrete sample space and computing expected value by weighting payoffs against their probabilities.

To solve problems of this type, you identify all possible outcomes (here, the 36 equally likely results from rolling two dice), classify which outcomes satisfy a condition (in this case, whether the sum is prime), assign payoffs accordingly, and then compute the probability-weighted average. The question rewards careful enumeration and clean arithmetic as much as conceptual understanding.

• Sample space enumeration and symmetry
• Prime number recognition and filtering
• Linearity of expectation and weighted averaging
• Simplifying fractions to lowest terms