# I love 5! Sorry for being unfair.

Discrete Mathematics Level pending

I have an unfair $$6$$-sided die. Its faces were numbered with integers $$1$$, $$2$$, $$3$$, $$4$$, $$5$$, and $$6$$. I rolled the die $$2$$ times. Let $$A$$ be the value of the first roll and $$b$$ be the value of the second roll. The probability that $$A$$ and $$B$$ will be both equal to $$5$$ $$OR$$ $$A$$ and $$B$$ will be distinct integers is $$\frac{241}{245}$$. If the smallest possible probability (minimum value) of rolling a $$5$$ in the die is in the form $$\frac{m}{n}$$ where $$m$$ and $$n$$ are coprime positive integers. Find $$m + n$$

Details and Assumptions:

• The die in this problem is unfair. Each of the probabilities of rolling a $$1$$, $$2$$, $$3$$, $$4$$, $$5$$, and $$6$$ are not all equal to each other.

• If I get $$2$$ in the first roll and $$5$$ in the second roll, then $$A = 2$$ and $$B = 5$$

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