Three coats of paint are sprayed onto a surface. The thicknesses, in millimetres, of the three coats have independent distributions $N\left( {0.13,{\text{ }}{{0.02}^2}} \right)$, $N\left( {0.14,{\text{ }}{{0.03}^2}} \right)$ and $N\left( {0.10,{\text{ }}{{0.01}^2}} \right)$. Find the probability that, at a randomly chosen place on the surface, the total thickness of the three coats of paint is less than 0.30 millimetres.
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