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 As a UC Berkeley CS student, you’re always thinking about ways to become the next billionaire in Silicon Valley. After hours of brainstorming, you’ve finally cut your list of ideas down to 10, all of which you want to implement at the same time. A venture capitalist has agreed to back all 10 ideas, as long as your net return from implementing the ideas is positive with at least 95% probability. Suppose that implementing an idea requires 50 thousand dollars, and your start-up then succeeds with probability p, generating 150 thousand dollars in revenue (for a net gain of 100 thousand dollars), or fails with probability 1 − p (for a net loss of 50 thousand dollars). The success of each idea is independent of every other. What is the condition on p that you need to satisfy to secure the venture capitalist’s funding?

 

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