Decision-making, in the interview

Expected value: weigh each outcome by its odds

Expected value multiplies each possible outcome by its probability and adds them up, so a likely small gain and an unlikely large one can be compared on one scale. In an interview it is the cleanest way to answer a risk question: put rough odds and payoffs on each option, then say what the numbers do not capture.

How does Expected value work?

List the options and, for each, the outcomes that matter.
Put a rough probability and a value on each outcome. Say they are estimates.
Multiply and add: expected value = (chance of gain x gain) minus (chance of loss x loss).
Adjust for what the average hides: a loss you could not survive, or a firm's appetite for risk.

When does Expected value fit an interview question?

It fits any question that gives you options with uncertain payoffs: two projects, a bet on a new market, an investment against a cost saving. Interviewers care less about the arithmetic than about you naming the probabilities and the assumption behind each one.

What does a strong answer with Expected value sound like?

Question: project A has a high chance of moderate success; project B has a low chance of transforming the business. You can fund one.

"Rough numbers: A is an 80% chance of adding 10 million, so about 8 million expected. B is a 10% chance of 200 million, so about 20 million expected. B wins on expected value, but the average hides the 90% case where we get nothing. If the company can survive that, I fund B in stages with kill points. If it cannot, A."

Common mistakes

Presenting made-up probabilities as facts instead of labeled estimates.
Stopping at the average and ignoring a downside the company cannot survive.
Doing long arithmetic out loud instead of round numbers and a conclusion.

Where does Expected value come from?

The idea dates back to the 1654 letters between Blaise Pascal and Pierre de Fermat on how to split the stakes of an unfinished game of chance. Christiaan Huygens published it in 1657. It is now the basis of decision analysis, finance and insurance.

Practice with this framework

These problems from the free GCA practice set are best answered with Expected value. Pick the framework that fits each one, then read the worked answer.

5 questions, one at a time

Pick a pace. The timer stops when you check an answer, and the worked method opens straight away. Nothing is saved or sent anywhere.

Pace

Interview pace4 min per question, like the real roundSprint90 seconds per questionNo timerTake as long as you need

Keys: 1 to 4 pick an option, Enter checks and moves on.

One question, two answers

A weak answer, why it scores low, and the strong one. Under a minute each.

Acquisition or retention?
The safe bet or the moonshot

Expected value: FAQ

How do you calculate expected value?

Multiply each outcome by its probability and add the results. For a simple bet: (probability of gain x size of gain) minus (probability of loss x size of loss). A positive result means the bet pays on average.

Why is expected value not enough on its own?

Because it is an average. A choice with a high expected value can still carry a small chance of a loss you cannot recover from, so strong answers pair it with a check on the worst case and the firm's appetite for risk.