A bag contains \(19\) unbiased coins and one coin with head on both sides. One coin drawn at random is tossed and head t…

A bag contains \(19\) unbiased coins and one coin with head on both sides. One coin drawn at random is tossed and head turns up. If the probability that the drawn coin was unbiased, is \(\frac{\mathrm{m}}{\mathrm{n}},\gcd (\mathrm{m},\mathrm{n})=1\), then \({n}^{2}-{m}^{2}\) is equal to :

[JEE Main 2025, 7 Apr (Shift 2)]