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Probability Deal Acceptance

MediumStatistics & Probability00:00
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Your question is Probability Deal Acceptance. Take a moment with it on the right.

Talk me through your thinking if you like. When you're confident, submit your answer and I'll grade it like a real screen (7/10 or better passes).

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Problem

A friend offers you a deal: they will pay you back $100 with a 50% chance, and if they do, you also get $10 the next day. Would you accept this deal?

Assume you must lend your friend $100 today and receive either $110 total or nothing later. Calculate the expected net payoff, compare it with the amount lent, determine the break-even repayment probability, and state whether you would accept the deal based on expected monetary value. Also identify any practical considerations that expected value alone does not capture.