Danny decides to roll an 8 sided die (with sides numbered 1-8)
Ted decides to roll two 4 sided dice (each with sides numbered 1-4)
What is the probability that Danny's roll will be more than the sum of Ted's rolls?
If the answer is a fraction, where and are coprime positive integers give the answer as .
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The probability is given by
P ( 8 > 2 × 4 ) = ∑ 2 8 P 4 ( n ) P 8 ( n )
Where,
P 4 ( n ) = Probability of rolling a total of n with two four sided die.
P 8 ( n ) = Probability of rolling something higher than n with an eight sided die.
So
P ( 8 > 2 × 4 ) = 1 6 1 ⋅ 8 6 + 1 6 2 ⋅ 8 5 + 1 6 3 ⋅ 8 4 + 1 6 4 ⋅ 8 3 + 1 6 3 ⋅ 8 2 + 1 6 2 ⋅ 8 1 + 1 6 1 ⋅ 0 = 8 3
3 + 8 = 1 1