Calculate probability using P(A) = 1-P(not A)
", "licence": "None specified"}, "statement": "Two $\\var{n}$-sided dice, each with sides labelled $1,2...\\var{n}$ are rolled and their scores are added.
We are looking for pairs of numbers than total to make $\\var{min[choice]}$ or less, which is quite a small total, so it doesn't take too long to find that the pairs of numbers are:
\n\\[ \\var{pairstruncate} \\]
\nso there {isorare} $\\var{pairschoice[choice]+1}$ {event} we are interested in, and therefore the probability is
\\[ P(\\text{total is} \\leq \\var{min[choice]}) = \\frac{\\var{pairschoice[choice]+1}}{\\var{total}} \\]
There are a very large number of ways to totals of $\\var{min[choice]+1}$ or greater, so in this case we use the complement rule;
\\[P(A') = 1-P(A)\\]
which in this case means
\n\\[P(\\text{total is}\\ge \\var{min[choice]+1}) = 1-P(\\text{total is} \\leq \\var{min[choice]}) = 1-\\frac{\\var{pairschoice[choice]+1}}{\\var{total}} = \\var[fractionnumbers]{1-options[choice]/{total}}\\]
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\n\n[[0]] (Give your answer as a fraction)
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Hint: It will probably save you time if you use the complement rule.
\n
[[0]] (Give your answer as a fraction)
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