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Seven standard, six-sided dice are rolled, one after the other. What is the probability that:

a) exactly one of them shows a six?
c) there is at least one that shows a six?

  • Math -

    prob(6) = 1/6
    prob(not6) = 5/6

    a) exactly 1 out of 7 tries to be 6
    = C(7,1) * (1/6)^1 * (5/6)^6
    = .3907 rounded to 4 decimals

    b) at least one 6 ---> 1 - prob(all not6)
    = 1 - C(7,7) * (1/6)^0 * (5/6)^7
    = 1 - .2791
    = .7209

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