Sunday, September 20, 2009

Triple 6

You throw three dice n times. How big does n have to be for you to have greater than a 50% chance of throwing three 6's?
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  1. DavidSeptember 22, 2009 at 10:57 AM

    The answer is 150.

    If three dice are thrown, the probability of NOT getting triple sixes is 1-(1/6)^3 = 215/216. So the probability of not getting triple sixes in n throws is (215/216)^n

    Now we solve an inequality.
    (215/216)^n < 0.5
    log[(215/216)^n] < log(0.5)
    n * log(215/216) < log(0.5)
    n > log(0.5)/log(215/216) = 149.37...
    n >= 150

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