Dicey Probability

Satvik and Agnishom are playing a game with \(2\) standard dice. Both the dice are rolled together and the total is counted.

Satvik says that a total of \(2\) will be rolled first.

Agnishom, whereas, says that two Consecutive totals of \(7's\) will be rolled first.

They keep rolling the dice till one of them wins!

The probability that Satvik wins the game can be expressed as \(\dfrac{a}{b}\) where \(a\) and \(b\) are co-prime positive integers.

Find the value of \(a+b\).


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