Expected Value Questions That Appear in Trading Interviews

Expected value interview questions test whether you can price a gamble correctly, subtract the entry cost, and size the bet that follows.

Expected value questions test whether a candidate can turn a described gamble into a single number under time pressure. Interviewers at prop trading firms use them to check three things at once: whether you multiply each outcome's probability by its payoff correctly, whether you remember to subtract the cost of playing, and whether you can explain the arithmetic out loud while someone watches and interrupts you.

Expected value is the probability-weighted average of every possible outcome of a bet. You list each outcome, multiply its payoff by the probability it occurs, and add the results together. A game that pays $100 with probability 0.3 and $0 otherwise has an expected value of $30, because 0.3 times 100 equals 30 and the remaining branch contributes nothing.

The interviewer already knows you can define expected value. What they are watching for is whether you set up the branches correctly before you start multiplying, whether you keep the entry cost separate from the payoff, and whether you say the final number with confidence rather than trailing off into a guess.

A common opening question: a fair coin is flipped once. Heads pays $25, tails pays $0, and it costs $10 to play. The expected payoff is 0.5 times 25 plus 0.5 times 0, which is $12.50. Subtracting the $10 entry price leaves an expected profit of $2.50 per play, so the correct answer is to take the bet.

A slightly harder version replaces the coin with a die. You roll a fair six sided die and are paid the face value in dollars, except a roll of 1 pays nothing. The expected value is one sixth of 0, plus one sixth of 2, plus one sixth of 3, plus one sixth of 4, plus one sixth of 5, plus one sixth of 6. Those payoffs sum to 20, and 20 divided by 6 is approximately $3.33. If the interviewer then quotes an entry price of $3, the expected profit is about 33 cents, thin but still positive.