Should you play a dice payout game?
Company: PayPal
Role: Data Scientist
Category: Statistics & Math
Difficulty: easy
Interview Round: Onsite
Two players each roll a fair six-sided die once.
- If **you win** (your roll > opponent’s roll), the opponent pays you **$n**.
- If the **opponent wins or it’s a tie** (your roll ≤ opponent’s roll), you pay the opponent **$m**.
Assume both dice are fair and independent.
## Questions
1) What is the **expected value** of playing one round as a function of `n` and `m`?
2) For what values of `n` and `m` should you **choose to play**?
3) (Optional) Show a short Python snippet that computes the expected value analytically.
Overview: This question evaluates understanding of probability, expected value, and payoff-driven decision-making by requiring computation of expected return from discrete game outcomes. It is commonly asked to assess quantitative reasoning in the Statistics & Math category and primarily tests conceptual understanding of expected value and probabilistic reasoning rather than practical implementation.
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