Compute expected value of simple gambling games
Company: J.P. Morgan
Role: Data Scientist
Category: Software Engineering Fundamentals
Difficulty: easy
Interview Round: Technical Screen
You are asked two probability/EV questions.
## 1) Dice game expected value / fair entry fee
A game works as follows:
- You pay an entry fee of \(c\) dollars to play.
- You roll a fair six-sided die once.
- If the die shows \(k\in\{1,2,3,4,5,6\}\), you receive \(k\) dollars as your payout.
**Questions**
1. What is the expected payout (in dollars)?
2. What is the expected net profit (payout minus entry fee)?
3. What is the largest entry fee \(c\) you should be willing to pay if you want the expected net profit to be \(\ge 0\)?
## 2) Alternating coin tosses: first head wins
Two players alternate flipping a fair coin. Player A flips first.
- The first player to flip **Heads** wins immediately.
**Question**: What is the probability that Player A wins?
Quick Answer: This question evaluates a candidate's ability to compute expected value and reason about sequential probabilities in simple gambling scenarios, covering competencies in expectation calculation, net payoff/fair entry fee determination for a die roll, and first-success probability for alternating coin tosses.