Problems 001

Welcome to a new, short series of problems, presented here for your, uh, not sure what...

Say you have access to a repeatable experiment whose favorable outcome, utterly randomly determined, is very unlikely--like a state lottery. Say the likelihood of "winning" (whatever that means) is 1 in 1,000,000,000. OK, you repeat it 1,000,000,000 (same number as above) times. What is the likelihood that you still haven't won it even once? What is the likelihood that you have won it exactly once. (1 minus the sum of those two is the likelihood that you have won it two or more times, ending with the very, very small probability that you have won it every single time, or 1,000,000,000 times in all.)


  1. Surely the answer to the first question is the chance of not winning it, to the power of the number of times?

    (1 - 1/1000000000)^1000000000

    =~ 0.37

  2. Both will be approximately 1/e ≈ 0.368.


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