Even 4 dice can create havoc

Probability Level 5

Four regular non-identical dice are rolled. The probability that the outcome is more than 1414 is of the form AB\dfrac{A}{B}, where AA and BB

are co-prime integers.

Find the value of BAB-A.

Details and Assumptions\textbf{Details and Assumptions}

  • Outcome means

    n=14(number appearing on nth die) \displaystyle\sum_{n=1}^{4}(\text{number appearing on} \ n^{\text{th}} \ \text{die})

  • The four dice are regular ones, numbered 1, 2, , 61, \ 2, \ \cdots , \ 6.

  • The four dice are not identical. You can consider them to be of four different colors.

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