\(100\) identical coins each with probability \(P\) of coming Heads are tossed simultaneously. If \(0<P<1\) and the probability of Heads coming on \(50\) coins is equal to that of Heads coming on \(51\) coins, then the value of \(P\) can be expressed as \(\dfrac{a}{b}\).

Find the value of \(100000\times(a+b)\).

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