Oct 08, 2026 by Offer

Probability: expected value (With Examples): Interview Answer Guide 2027

Expected value is the probability-weighted average of all possible outcomes: multiply each outcome by its probability and add them up. A correct expected value interview question answer states the formula EV = Σ (probability × payoff), then applies the decision rule — take bets with positive expected value, skip negative ones — while noting that real decisions also weigh risk tolerance and bankroll.

What the Expected Value Interview Question Tests

Whether you can compute EV cleanly: probabilities times payoffs, summed, with correct signs for losses.
Whether you know the decision rule — positive EV is worth taking — and its limits in real life.
Whether you confuse expected value with the most likely outcome; they are often different.

How to Answer the Expected Value Interview Question

Work the numbers out loud — interviewers grade the process:

Example 1 — coin flip. Win $10 on heads (p=0.5), lose $10 on tails (p=0.5). EV = 0.5(10) + 0.5(−10) = $0. A fair game.
Example 2 — biased offer. Win $20 on heads (p=0.5), lose $10 on tails (p=0.5). EV = 10 − 5 = $5. Take it every time.
Example 3 — dice game. Roll a fair die; you win $12 on a 6, lose $2 otherwise. EV = (1/6)(12) + (5/6)(−2) = 2 − 1.67 = $0.33. Slightly positive — worth playing if the stakes are small relative to your bankroll.

Sample close: "The pattern is always the same: probabilities times payoffs, summed, then compared against what the bet costs you."

Common Mistakes With the Expected Value Interview Question

Forgetting that probabilities must sum to 1. If they don't, your EV is fiction.
Treating EV as a prediction of one trial. EV describes the average over many repetitions, not what happens next time.
Ignoring variance: a positive-EV bet that can wipe you out is still a bad bet if you cannot survive the downswings.

Trading firms live on expected value, so they expect you to compute it fast and talk about it sensibly. Candidates who blurt a number without checking signs, or who cannot explain why a +EV bet can still be wrong, rarely make it past the first round.

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FAQ

What is the formula for expected value?

EV = Σ [P(outcome) × value(outcome)]. List every possible outcome, multiply each by its probability, and sum the results.

What is a simple expected value example?

A fair six-sided die pays you the number shown in dollars. EV = (1+2+3+4+5+6)/6 = $3.50. Paying $3 to play is +EV; paying $4 is −EV.

Should you always take positive expected value bets?

In theory yes, repeated often. In practice, consider variance and ruin risk — a +EV bet that risks your entire bankroll can still be the wrong choice.

What is the difference between expected value and the most likely outcome?

The most likely outcome is the mode; EV is the weighted average. A lottery's most likely outcome is winning nothing, while its EV is the ticket price minus the house edge.

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