Statistics · easy
Asked in Data Scientist interviews, in the Statistics round.
Expected value is the probability-weighted average of the outcomes. A ticket that pays 1,000 with probability 0.001 has an expected value of 1, a number you never actually win. It is the long-run average per play, not what happens on any one play.
Expected value is the average outcome weighted by probability: sum each outcome times its chance. For a fair die it is 3.5, a value the die never shows.
The interviewer's follow-up is always some version of "so should you take the bet". A coin flip that pays 3 on heads and costs 2 on tails has an expected value of 0.5 per flip, positive, so over a thousand flips you come out ahead with near certainty. A single flip is still a 50% chance of losing 2. Expected value is a long-run statement, and the variance says how rough the road is.
Where it lands in the job: lifetime value is an expected value over churn probabilities, the expected cost of a fraud model is false positive rate times review cost plus miss rate times loss, and a promotion's expected lift is the sum over segments weighted by their share. In each case you should say the variance too. A decision with a good average and a chance of ruin is not a good decision.