Jane Street–styleTraderAssistant TraderQuestion #205

You have a dartboard that is split in half. If you hit the left half, you get 2 points; if you hit the right half, you get 3 points. You have an 80% chance of hitting the dartboard on any given throw and, if you hit the board, a 70% chance of hitting the side you are aiming for (and a 30% chance of hitting the other side). With an unlimited number of throws, what is the probability that you achieve a score of exactly 7?

Build Your Approach

State the assumptions, try a simple case, then work toward a general solution. Check the result and explain how it changes if an assumption changes.

Try the free diagnostic with worked solutions →

Get Free Interview Prep Resources

Practice the Reasoning Behind the Answer

Bring your target roles and interview timeline to a free quant consult. Discuss your preparation priorities and how Quant Blueprint’s lessons, practice and mock interviews can help.

Book a Free Quant Consult

Your goals · your preparation · your next steps